Unsaturated Flow Systems Research Articles

Impact of coupled heat transfer and water flow on soil borehole thermal energy storage (SBTES) systems: Experimental and modeling investigation

A promising energy storage option is to inject and store heat generated from renewable energy sources in geothermal borehole arrays to form soil-borehole thermal energy storage (SBTES) systems. Although it is widely recognized that the movement of water in liquid and vapor forms through unsaturated soils is closely coupled to heat transfer, these coupled processes have not been considered in modeling of SBTES systems located in the vadose zone. Instead, previous analyses have assumed that the soil is a purely conductive medium with constant hydraulic and thermal properties. Numerical modeling tools that are available to consider these coupled processes have not been applied to SBTES systems partly due to the scarcity of field or laboratory data needed for validation. The goal of this work is to test different conceptual and mathematical formulations that are used in heat and mass transfer theories and determine their importance in modeling SBTES systems. First, a non-isothermal numerical model that simulates coupled heat, water vapor and liquid water flux through soil and considers non-equilibrium liquid/gas phase change was adopted to simulate SBTES systems. Next, this model was used to investigate different coupled heat transfer and water flow using nonisothermal hydraulic and thermal constitutive models. Data collected from laboratory-scale tank tests involving heating of an unsaturated sand layer were used to validate the numerical simulations. Results demonstrate the need to include thermally induced water flow in modeling efforts as well as convective heat transfer, especially when modeling unsaturated flow systems. For the boundary conditions and soil types considered, convective heat flux arising from thermally induced water flow was greater than heat transfer due to conductive heat flux alone. Although this analysis needs to be applied to the geometry and site conditions for SBTES systems in the vadose zone, this observation indicates that thermally induced water flow can have significant effects on the efficiency of heat injection and extraction.

Preliminary Study on the Effects of Surface Microtopography on Tracer Transport in a Coupled Overland and Unsaturated Flow System

AbstractSurface microtopography influences both spatial and temporal distributions of a series of hydrologic processes including infiltration, surface runoff, and unsaturated flow. Importantly, surface roughness and depressions also affect the fate and transport of pollutants throughout surface and subsurface environments. The objective of this study was to experimentally investigate the effects of surface microtopography on overland flow, infiltration, and tracer bromide (Br) runoff, and leaching into the subsurface system under simulated rainfall. Both rough and smooth surfaces were created by using sieved soil and scanned by an instantaneous-profile laser scanner to acquire high-resolution digital elevation models (DEMs) of the soil surfaces. A mold surface, featuring a number of depressions of varied sizes and relationships, was used to create the rough soil surface. The Windows-based puddle delineation (PD) software was applied to characterize surface microtopography, determine flow directions and ac...

A review on soil cover in waste and contaminant containment: design, monitoring, and modeling

Soil cover is a widely-used but relatively new method for solid waste containment. Standard while site-specific procedures for cover design, monitoring, and evaluation are needed to insure reliable cover performance. This paper presents a review of soil cover types, design principles and procedures, cover monitoring, and long-term performance modeling. Cover types and cover design are introduced with the general concepts and discussed on their specific applicabilities in different circumstances. Detailed discussion is given on unsaturated flow system properties and their field measurements, including methods, apparatuses/equipments and their advantages and disadvantages. Several unsaturated flow simulators are discussed and compared with regards to their simulation capacities for critical parameters closely related to soil cover performance such as runoff, infiltration and evaporation. Finally, research subjects are suggested for future work for better soil cover monitoring and modeling.

Investigation of Episodic Flow from Unsaturated Porous Media into a Macropore

The recent literature contains numerous observations of episodic or intermittent flow in unsaturated flow systems under both constant flux and ponded boundary conditions. Flow systems composed of a heterogeneous porous media, as well as discrete fracture networks, have been cited as examples of systems that can exhibit episodic flow. Episodic outflow events are significant because relatively large volumes of water can move rapidly through an unsaturated system, carrying water and contaminants to depth greatly ahead of a wetting front predicted by a one‐dimensional, gravity‐driven diffusive infiltration model. In this study, we model the behavior of water flow through a sand column underlain by an impermeable‐walled macropore. Relative permeability and capillary pressure relationships were developed that capture the complex interrelationships between the macropore and the overlying porous media that control flow out of the system. The potential for episodic flow is assessed and compared to results of conventional modeling approaches and experimental data from the literature. Model results using coupled matrix–macropore relative permeability and capillary pressure relationships capture the behavior observed in laboratory experiments remarkably well, while simulations using conventional relative permeability and capillary pressure functions fail to capture some of the observed flow dynamics. Capturing the rapid downward movement of water suggests that the matrix‐macropore capillary pressure and relative permeability functions developed have the potential to improve descriptions of flow and transport processes in heterogeneous, variably saturated media.

Research Advances in Vadose Zone Hydrology through Simulations with the TOUGH Codes: Preface from the Guest Editors

Numerical simulators are playing an increasingly important role in advancing our fundamental understanding of hydrological systems. They are indispensable tools for managing groundwater resources, analyzing proposed and actual remediation activities at contaminated sites, optimizing recovery of oil, gas, and geothermal energy, evaluating subsurface structures and mining activities, designing monitoring systems, assessing the long-term impacts of chemical and nuclear waste disposal, and devising improved irrigation and drainage practices in agricultural areas, among many other applications. The complexity of subsurface hydrology in the vadose zone calls for sophisticated modeling codes capable of handling the strong nonlinearities involved, the interactions of coupled physical, chemical and biological processes, and the multiscale heterogeneities inherent in such systems. The papers in this special section of ''Vadose Zone Journal'' are illustrative of the enormous potential of such numerical simulators as applied to the vadose zone. The papers describe recent developments and applications of one particular set of codes, the TOUGH family of codes, as applied to nonisothermal flow and transport in heterogeneous porous and fractured media (http://www-esd.lbl.gov/TOUGH2). The contributions were selected from presentations given at the TOUGH Symposium 2003, which brought together developers and users of the TOUGH codes at the Lawrence Berkeley National Laboratory (LBNL) inmore » Berkeley, California, for three days of information exchange in May 2003 (http://www-esd.lbl.gov/TOUGHsymposium). The papers presented at the symposium covered a wide range of topics, including geothermal reservoir engineering, fracture flow and vadose zone hydrology, nuclear waste disposal, mining engineering, reactive chemical transport, environmental remediation, and gas transport. This Special Section of ''Vadose Zone Journal'' contains revised and expanded versions of selected papers from the symposium, with special attention to issues related to the vadose zone and unsaturated flow systems. The first paper, written by the original developer of TOUGH, Karsten Pruess, provides an overview of the history of the TOUGH codes, the main physical processes considered, their mathematical and numerical implementation, and case studies. That paper is followed by a review article summarizing inverse modeling applications performed by iTOUGH2. A subsequent group of papers deals with diverse unsaturated zone systems, highlighting the versatility of the code to handle a variety of processes in different geologic settings. Simulation capabilities of the TOUGH codes are increasingly used for geologic carbon sequestration studies as testified by the next group of papers. The final series of papers demonstrates the use of the TOUGH codes in support of remediation and engineering applications. These studies discuss biological and reactive chemical transport simulations, the design of clean-up operations and landfill management, and the analysis of engineered soil stabilization. As guest editors, we thank the authors for their interesting contributions, and the many reviewers for their careful and constructive review comments. Finally, on behalf of all of the authors and ourselves, we express our sincerest appreciation to Rien van Genuchten for providing the opportunity to publish these papers together in a Special Section of ''Vadose Zone Journal''.« less

Type curves and effective parameters for unsaturated flow systems with structured heterogeneities

Unsaturated flow simulation requires identification of soil parameters at length scales that usually subsume smaller-scale heterogeneities. The standard two-parameter constitutive model performs well for predictions of moisture plume evolution in homogeneous soils but may not be as successful in capturing the flow and dispersion of soil water in heterogeneous domains. The first step in evaluating the limitations of this model is to develop a clear understanding of the effects of the constitutive parameters on moisture plume evolution. One approach is to define type curves derived from multiple homogeneous simulations. These type curves are based on bulk measures of system behavior, suitable for comparison to responses of heterogeneous systems. Simulation results for a range of heterogeneities defined on a specific test system indicate that some heterogeneity patterns allow definition of effective parameters for use in the two-parameter constitutive model, while others do not. For those heterogeneity patterns, the mathematical structure of the governing equations applied at the large scale must have a form that is different from the equation that underlies the type curves.

Mechanistic modeling of fingering, nonmonotonicity, fragmentation, and pulsation within gravity/buoyant destabilized two‐phase/unsaturated flow

Fingering, nonmonotonicity, fragmentation, and pulsation within gravity/buoyant destabilized two‐phase/unsaturated flow systems has been widely observed with examples in homogeneous to heterogeneous porous media, in single fractures to fracture networks, and for both wetting and nonwetting invasion. To model this phenomena, we consider a mechanistic approach based on forms of modified invasion percolation (MIP) that include gravity, the influence of the local interfacial curvature along the phase‐phase interface, and the simultaneous invasion and reinvasion of both wetting and nonwetting fluids. We present example simulations and compare them to experimental data for three very different situations: (1) downward gravity‐driven fingering of water into a dry, homogeneous, water‐wettable, porous medium; (2) upward buoyancy‐driven migration of gas within a water saturated, heterogeneous, water‐wettable, porous medium; and (3) downward gravity‐driven fingering of water into a dry, water‐wettable, rough‐walled fracture.

Numerical analysis of flow and transport in a combined heterogeneous vadose zone–groundwater system

Numerical simulations of water flow and solute transport were used to investigate the effect of the recharge (rain/irrigation) at the soil surface on solute spreading and breakthrough in a realistic, three-dimensional, heterogeneous, vadose zone–groundwater flow system. Results of the analyses suggest that smaller recharge at the soil surface increases the relative variability in the response of the unsaturated flow system, decreases the groundwater recharge from the unsaturated zone, and, concurrently, decreases the degree of nonuniformity of the groundwater flow. Consequently, smaller recharge at the soil surface enhances the longitudinal and, especially the transverse spreading of the solute plume and increases the spreading of the expected solute BTC at the lower boundary of the unsaturated zone. Furthermore, smaller recharge at the soil surface decreases the extent of the vertical penetration of the solute plume into the groundwater, slows the peak arrival of the expected BTC, and considerably increases the spreading of the expected solute BTC at a given vertical control plane in the saturated region. It was shown that for the combined flow system considered here in which the solute plume is displaced to a sufficiently large vertical distance from the inlet zone at the soil surface, the variable that controls the transport is the cumulative recharge at the soil surface, and not the recharge rate.

Modelling subsurface flow conditions in a salinized catchment in south-western Australia, with a view to improving management practices

Finite element modelling of the saturated–unsaturated surface–subsurface flow mechanisms operative in a small salinized catchment in south-western Australia was used to help define the flow system and explain the causes of waterlogging and salinization there. Data available at the site from a previous study were used to obtain a first approximation to the flow system. Altering the properties of some of the strata gave a closer calibration. It was found that the modelled saturated hydraulic conductivity of the B horizon in the duplex soil zone needed to be at least an order of magnitude lower than that measured in order to reproduce the perching conditions observed in the field. Also, the model indicated the influence of a doleritic dyke, whose presence was confirmed by field measurement. Our analysis showed that there were two main flow systems operating in the hillslope. The first, and most dominant, was the recharge occurring through the upslope gradational soil zone and percolating down to both the deeply weathered regolith and the basal aquifer. The second flow system is an unsaturated flow system operating in the high permeability A horizon in the downslope duplex soil zone. The first system is primarily responsible for the saline seepage zone in the valley bottom. The second contributes to the waterlogging and perching occurring upslope of the seepage zone. Vertical flow through the higher permeability B horizon in the gradational soil zone in the upper slopes is a major contributor of recharge. Recharge by flow through macropores occurs where, but only where, perched aquifers develop and allow the macropores to be activated. Areas with perched aquifers occurred in downslope locations and near a doleritic dyke located upslope. Thus, the area where macropore recharge occurred was not large. The recharge rate required to maintain the piezometric levels at present values is only about 30 mm/yr (about 5% of the annual rainfall). The piezometric levels under the upper part of the catchment varied greatly with only small changes in recharge rate. A 50% reduction in recharge rate had the effect of reducing the length of the seepage zone at the end of winter by 40%. Changes in recharge rate had little effect on the extent of the perched aquifer at the end of winter. Deep-rooted perennial forages, shrubs or trees on the gradational soil zone in the upper part of the catchment and on the zones upslope of geological barriers to flow would be required to reduce the recharge and to allow for rehabilitation of the saline valley floor. Waterlogging associated with the perched water table in the bottom part of the catchment would be best addressed by tree plantations located just upslope of the salinized zone in the valley floor. Copyright © 1999 John Wiley & Sons, Ltd.

Unsaturated water flow around obstructions simulated by two-dimensional Rankine bodies

Unsaturated flow systems were studied which consisted of two-dimensional doublets embedded in a porous medium. The isolated flow regions formed around the doublets (source-sink combinations) were called Rankine bodies as a generalization of the classical geometries used in fluid mechanics for solutions to Laplace's equation. The motivation was to simulate unsaturated flow around subterranean objects, such as cavities and rock inclusions. The results were generally successful and patterns for single inclusions qualitatively matched more elaborate solutions based on scattering theory. A complex system (of five inclusions) was presented to simulate a layered case of rock inclusions within a profile.

Application of stochastic unsaturated flow theory, numerical simulations, and comparisons to field observations

A stochastic unsaturated flow theory and a numerical simulation model have been coupled in order to estimate the large‐scale mean behavior of an unsaturated flow system in a spatially variable soil. On the basis of the theoretical developments of Mantoglou and Gelhar (1987a, b, c), the theory assumes that the local hydraulic soil properties are realizations of three‐dimensional random fields, and it derives the large‐scale flow structure by averaging the local governing flow equation over the ensemble. The resulting mean model representation is in the form of a partial differential equation, similar to the local flow equation, in which effective model parameters occur (e.g., effective hydraulic conductivity). Further, the theory predicts the variance (prediction error) of the capillary tension head due to the spatial variability of the local hydraulic soil properties. The governing unsaturated flow equation representing the mean system behavior is solved using a finite difference numerical solution technique. The effective parameters are evaluated from the stochastic theory formulas before entering them into the numerical solution for each iteration. The stochastic model is applied to a field site in Denmark, where information is available on the spatial variability of soil parameters and variables. Numerical simulations have been carried out, and predictions of the mean behavior and the variance of the capillary tension head and the soil moisture content have been compared to field observations. The stochastic model predicts the average system behavior reasonably well. Reasonable results are also obtained for the range of variation of the capillary tension head, despite the limited number of measurements and corresponding statistical inference issues. The stochastic model presented here seems to offer a rational framework for modeling large‐scale unsaturated flow and estimating areal averages of soil‐hydrological processes in spatially variable soils.

Statistical Parameters Characterizing the Spatial Variability of Selected Soil Hydraulic Properties

AbstractThe knowledge of the statistical parameters of the variance, σ2, and the correlation scale, λ, characterizing the spatial structures of the log of the saturated hydraulic conductivity, lnKs, pore size distribution parameter α, and the specific water capacity, C, is required in stochastic modeling in order to understand the overall response of large‐scale heterogeneous unsaturated flow systems. These parameters are estimated assuming second‐order stationarity and an exponential semivariogram model with nugget effect. Methods of ordinary least squares (OLS), maximum likelihood (ML), and restricted maximum likelihood (RML) are used for estimating σ2 and λ, while methods of cross‐validation (kriging) and uncorrelated residuals are used to validate the semivariogram model with estimated σ2 and λ. The objectives of this study were to evaluate the sensitivity of σ2 and λ to the estimation methods and to discuss the implications of the analysis in view of the stochastic modeling. The significance of the results of parameter estimation and model validation in relation to the stochastic modeling of large‐scale transient unsaturated flow is demonstrated with two examples involving the variance of soil‐water pressure head, σ2h, and the vertical component of effective hydraulic conductivity, K*11. Results show that the estimated values of σ2 and λ are highly dependent on the estimation method. Although the majority of the estimated parameters pass the validation tests, the RML estimates of σ2 and λ used in estimating σ2h and K*11 significantly reduce the prediction uncertainties.

Stochastic modeling of large-scale transient unsaturated flow systems : Mantoglou, A; Gelhar, L W Water Resour ResV23, N1, Jan 1987, P37–46

Stochastic modeling of large-scale transient unsaturated flow systems : Mantoglou, A; Gelhar, L W Water Resour ResV23, N1, Jan 1987, P37–46

Stochastic modeling of large‐scale transient unsaturated flow systems

A new framework for modeling large‐scale transient unsaturated flow systems in spatially variable soils is proposed in order to overcome the problem of limited information about the local details of spatial soil variability. A stochastic approach, which assumes that local soil properties are realizations of three‐dimensional random fields, is followed for derivation of a large‐scale model representation (structure). The three dimensionality of the local flow and the nonlinear dependence of the local flow output on the local soil properties are considered. The large‐scale model structure is derived by averaging the local governing flow equation over the ensemble of realizations of the underlying soil property random fields. The resulting mean model representation is in the form of a partial differential equation in which averaged or effective model parameters occur. These effective model parameters (i.e., effective hydraulic conductivity and effective specific moisture capacity) are evaluated using a quasi‐linearized fluctuation equation and a spectral representation of stationary processes. The large‐scale model representation considers the large‐scale effects of soil property variability and has relatively few parameters. The general conclusions of this study are that soil property variability produces large‐scale hysteresis and anisotropy of the effective parameters. The potential theoretical and practical ramifications of these results in the area of unsaturated flow modeling need to be investigated. The general stochastic modeling framework developed here is applicable not only to unsaturated flow but also to other distributed parameter systems (e.g., saturated flow and transport, geothermal and oil reservoir modeling).

Measurements of the downslope flow of water in a soil

Measurements have been made of unsaturated and saturated lateral soil water flow on a convex hill-slope with a good soil cover and impermeable bedrock during natural rainstorms. The hydraulics of flow are examined in detail with particular reference to the role of breaks in vertical permeability, the change from saturated to unsaturated flow and the velocity of flow. In this instance, after rainfall slope flow is dominated by vertical unsaturated movement towards the profile base. Preceding upslope moisture gradients result in the growth of a zone of soil saturation upwards from the slope base. Slope discharge, through the B and B/C horizons, is related to the form of the saturation zone, within which flow is lateral, according to Darcy's law. The time required for vertical percolation and the low hydraulic conductivity of the lower soil horizons result in a hillslope hydrograph which is delayed and attenuated and cannot be regarded as stormflow. During drainage the saturation zone contracts and is replaced by a lateral unsaturated flow system at the profile base which supplies discharge from the B/C horizon for up to 42 days without further recharge. It is concluded that, in general, either distinct soil horizons or impermeable bedrock are essential for the initiation of lateral flow. Saturated flow is likely to dominate hillslope hydrographs through non-capillary pore spaces but these may be integrated to the point where Darcy's law still holds. Although lateral soil water flow must be a widespread phenomenon, it is unlikely to provide storm runoff to the stream unless saturated conditions are generated within the organic horizons for flow within the lower soil horizons is dominated by non-Darcian flow through non-capillary spaces in the soil.