Variably-saturated Porous Media Research Articles

Computational evaluations of HYDRUS simulations of drip irrigation in 2D and 3D domains (i-Surface drippers)

HYDRUS is a popular package for simulating water and solutes movement in variably-saturated porous media. It is widely used by designers of drip irrigation systems to simulate the active wetting pattern. However, there are many design parameters of the domain and for the flux calculation; other than the acceptable simulations, some configurations might cause under-estimation or over-estimation of the wetting pattern. Comparative assessments of the surface drip simulation parameters were performed. We evaluated the effect of different domain geometries, element shapes, coordinate systems, emitter discharges, and soil textures on the accuracy and stability of the simulation. The results showed that the 3D simulations are more successful and reliable than the 2D simulations in terms of mass balance error. For the 2D domains, the error increases as the texture goes finer, and for axisymmetric domains than the Cartesian ones. We found a relationship between the flux and the soil hydraulic conductivity that their quotient should not exceed 1.8 and 3.2 for axisymmetric and cartesian coordinates. Our outcomes show that the infiltration stage took more time than the redistribution stage because of the variation in water content that delays the convergence at infiltration.Additionally, we found that the range between the saturated and the residual water content of the soil causes instability of the simulation as it gets higher. The differences between 2D simulations and the equivalent 3D slices were highly dependent on the soil texture, the heavier the larger; and dependent on the simulation phase, where the redistribution phase has fewer differences than the infiltration phase. Finally, we have determined the best matching 2D flux profile to each 3D profile and revealed the source of variation between 2D and 3D profiles where it was mostly-affected by the emitter’s location, the soil texture, and simulation phase. In part 2 of this paper, we expanded the study for subsurface drip simulations and showed the difference between the two systems’ designs.

Modelling of Water Flow and Nitrate Dynamics Through Partially Saturated Porous Media in Laboratory Condition using Hydrus-2D

Due to the reducing availability of water resources and the growing competition for water between residential, industrial, and agricultural users, increasing irrigation efficiency, by several methods like drip irrigation, is a demanding concern for agricultural experts. The understanding of the water and contaminants flow through the subsurface is needed for the sustainable irrigation water management, pollution assessment, remediation, and groundwater recharge. In this study, the Windows-based computer software package HYDRUS-2D, which numerically simulates water and solute movement in two-dimensional, variably-saturated porous media, was used to evaluate the distribution of water and Nitrate in the sand tank. The laboratory and simulation experiments were conducted to evaluate the role of drainage, recharge flux, and infiltration on subsurface flow condition and subsequently, on nitrate movement in the subsurface. The water flow in the unsaturated zone was model by Richards’ equation, which was highly nonlinear and its parameters were largely dependent on the moisture content and pressure head of the partially saturated zone. Following different cases to be considered to evaluate- a) applying drainage and recharge flux to study domains, b) transient infiltration in a vertical soil column and c) subsequently, nitrate movement in a 2D sand tank setup. A single porosity model was used for the simulation water and nitrate flow in the study domain. The results indicate the transient water table position decreases as the time increase significantly by applying drainage flux at the bottom. Similarly, the water table positions in study domains increasing in the domain by applying recharge flux. Likewise, the water flow profile shows the decreasing water table elevation with increasing water content in the vertical domain. Furthermore, the nitrate transport dynamics was dominated by advective flux and highly affected by the recharge flux in the vertical direction. The findings of the study help to enhance the understanding of the sustainable soil-water resources management and agricultural practices.

RBFPUM with QR Factorization for Solving Water Flow Problem in Multilayered Soil

Abstract We discuss the numerical modeling of infiltration in variably-saturated porous media. Richards’ equation is used to describe the infiltration towards the water table. It is difficult to accurately approximate its solution especially when we deal with layered soil due to its highly nonlinear fact. In this work, the nonlinearity is handled by using Gardner model. In the case of homogeneous soil, the linearized equation is solved using radial basis function partition of unity method (RBFPUM) with the introduction of QR factorization of Gaussian in order to enhance the numerical solution for small values of the so-called “shape parameter.” In the case of layered soil, domain decomposition principle is introduced. It is based on decomposing the general problem into many subproblems. The latter are solved by RBFPUM-QR and patched by using the Steklov–Poincaré equation. Infiltration towards water table in homogeneous and layered soil is considered as a numerical test.

Radial basis function partition of unity method for modelling water flow in porous media

Water flow in variably-saturated porous media is modelled by using the highly nonlinear parabolic Richards’ equation. The nonlinearity is due to the hydraulic conductivity and moisture content variables. The latter were estimated by using experimental models, including Gardner, Burdine, Mualem and van Genuchten models. The aim of this work is to develop a new technique based on the radial basis function partition of unity method (RBFPUM) and Gardner model in order to solve Richards’ equation in one and two dimensions. We have used Gardner model to handle the nonlinearity issue and the RBFPUM is used to approximate the solution of the linearized Richards’ equation. Our proposed algorithm is based on testing many configurations of the partitions number and selecting the optimal shape parameter for each case. Then we pick up the optimal configuration (partitions number-shape parameter) that yields the best solution in terms of error and conditioning number. By following this procedure, an optimal solution is ensured for our given problem. As numerical tests, we consider the vertical infiltration of water in soils in order to validate our proposed method.

A computationally efficient pseudo-3D model for the numerical analysis of borehole heat exchangers

Ground-Source Heat Pump (GSHP) systems represent one of the most efficient renewable energy technologies. Their efficiency is highly influenced by the thermal properties of the ground, which are often measured in-situ using the Thermal Response Tests (TRTs). While three-dimensional mechanistic models offer significant advantages over analytical solutions for the numerical interpretation of TRTs, their computational cost represents a limiting factor. Moreover, most of the existing models do not include a comprehensive description of hydrological processes, which have proven to strongly influence the behavior of GSHP. Thus, in this study, we propose a computationally efficient pseudo-3D model for the numerical analysis and interpretation of TRTs. The numerical approach combines a one-dimensional description of the heat transport in the buried tubes of the exchanger with a two-dimensional description of the heat transfer and water flow in the surrounding subsurface soil, thus reducing the dimensionality of the problem and the computational cost. The modeling framework includes the widely used hydrological model, HYDRUS, which can simulate the movement of water, heat, and multiple solutes in variably-saturated porous media. First, the proposed model is validated against experimental data collected at two different experimental sites in Japan, with satisfactory results. Then, it is combined with the Morris method to carry out a sensitivity analysis of thermal properties. Finally, the model is exploited to investigate the influence of groundwater and lithologic heterogeneities on the thermal behavior of the GSHP.

Rapid imbibition of water in fractures within unsaturated sedimentary rock

The spontaneous imbibition of water and other liquids into gas-filled fractures in variably-saturated porous media is important in a variety of engineering and geological contexts. However, surprisingly few studies have investigated this phenomenon. We present a theoretical framework for predicting the 1-dimensional movement of water into air-filled fractures within a porous medium based on early-time capillary dynamics and spreading over the rough surfaces of fracture faces. The theory permits estimation of sorptivity values for the matrix and fracture zone, as well as a dispersion parameter which quantifies the extent of spreading of the wetting front. Quantitative data on spontaneous imbibition of water in unsaturated Berea sandstone cores were acquired to evaluate the proposed model. The cores with different permeability classes ranging from 50 to 500mD and were fractured using the Brazilian method. Spontaneous imbibition in the fractured cores was measured by dynamic neutron radiography at the Neutron Imaging Prototype Facility (beam line CG-1D, HFIR), Oak Ridge National Laboratory. Water uptake into both the matrix and the fracture zone exhibited square-root-of-time behavior. The matrix sorptivities ranged from 2.9 to 4.6mms−0.5, and increased linearly as the permeability class increased. The sorptivities of the fracture zones ranged from 17.9 to 27.1mms−0.5, and increased linearly with increasing fracture aperture width. The dispersion coefficients ranged from 23.7 to 66.7mm2s−1 and increased linearly with increasing fracture aperture width and damage zone width. Both theory and observations indicate that fractures can significantly increase spontaneous imbibition in unsaturated sedimentary rock by capillary action and surface spreading on rough fracture faces. Fractures also increase the dispersion of the wetting front. Further research is needed to investigate this phenomenon in other natural and engineered porous media.

A New Application of Dynamic Data Driven System in the Talbot-Ogden Model for Groundwater Infiltration

The TalbotOgden model is a mass conservative method to simulate flow of a wetting liquid in variably-saturated porous media. The principal feature of this model is the discretization of the moisture content domain into bins. This paper gives an analysis of the relationship between the number of bins and the computed flux. Under the circumstances of discrete bins and discontinuous wetting fronts, we show that fluxes increase with the number of bins. We then apply this analysis to the continuous case and get an upper bound of the difference of infiltration rates when the number of bins tends to infinity. We also extend this model by creating a two dimensional moisture content domain so that there exists a probability distribution of the moisture content for different soil systems. With these theoretical and experimental results and using a Dynamic Data Driven Application System (DDDAS), sensors can be put in soils to detect the infiltration fluxes, which are important to compute the proper number of bins for a specific soil system and predict fluxes. Using this feedback control loop, the extended TalbotOgden model can be made more efficient for estimating infiltration into soils.

Quantitative simulation on soil moisture contents of two typical vegetation communities in Sanjiang Plain, China

Different types of vegetation occupy different geomorphology and water gradient environments in the San- jiang Plain, indicating that the soil moisture dynamics and water balance patterns of the different vegetation communi- ties might differ from each other. In this paper, a lowland system, perpendicular to the Nongjiang River in the Honghe National Nature Reserve (HNNR), was selected as the study area. The area was occupied by the non-wetland plant forest and the typical wetland plant meadow. The Microsoft Windows-based finite element analysis software package for simulating water, heat, and solute transport in variably saturated porous media (HYDRUS), which can quantita- tively simulate water, heat, and/or solute movement in variably-saturated porous media, was used to simulate soil moisture dynamics in the root zone (20-40 cm) of those two plant communities during the growing season in 2005. The simulation results for soil moisture were in a good agreement with measured data, with the coefficient of determi- nation (R 2 ) of 0.44-0.69 and root mean square error (RMSE) ranging between 0.0291 cm 3 /cm 3 and 0.0457 cm 3 /cm 3 , and index of agreement (d) being from 0.612 to 0.968. During the study period, the volumetric soil moisture content of meadow increased with the depth and its coefficient of variation decreased with the depth (from 20 cm to 40 cm), while under the forest the soil moisture content at different depths varied irregularly. The calculated result of water budget showed that the water budget deficit of the meadow was higher than that of the forest, suggesting that the meadow is more likely to suffer from water stress than the forest. The quantitative simulation by HYDRUS in this study did not take surface runoff and plant growth processes into account. Improved root water uptake and surface

Numerical simulations of water movement in a subsurface drip irrigation system under field and laboratory conditions using HYDRUS-2D

Due to the decreasing availability of water resources and the increasing competition for water between residential, industrial, and agricultural users, increasing irrigation efficiency, by methods like subsurface drip irrigation (SDI) systems, is a pressing concern for agricultural authorities. To properly manage SDI systems, and increase the efficiency of the water/fertilizer use while reducing water losses due to evaporation, the precise distribution of water around the emitters must be known. In this paper, the Windows-based computer software package HYDRUS-2D, which numerically simulates water, heat, and/or solute movement in two-dimensional, variably-saturated porous media, was used to evaluate the distribution of water around the emitter in a clay loam soil. The simulation results were compared with two sets of laboratory and field experiments involving SDI with emitters installed at different depths, and were evaluated using the root-mean-square-error (RMSE). The RMSE at different locations varied between 0.011 and 0.045 for volumetric water contents, and between 0.98 and 4.36 cm for wetting dimensions. Based on these values, it can be concluded that the correspondence between simulations and observations was very good.

Modelling multiple solute transport in variably saturated soils : J. Simunek, M. T. Van Genuchten & D. L. Suarez, in: Groundwater quality: remediation and protection. Proc. conference, Prague, 1995, ed K. Kovar & J. Krasny, (IAHS; Publication, 225), 1995, pp 311–318

This paper presents two models typical of two different approaches often used for modelling the advective-dispersive transport of multiple ions in variably-saturated porous media. The first approach assumes that all solute reactions can be incorporated directly into the governing transport equations (the one-step method), while the second approach divides the mathematical solution process into two separate steps: one for transport, and one for most or all chemical reactions (the two-step method). The two approaches are illustrated using the one-step CHAIN_2D code which simulates the nonlinear nonequilibrium transport of solutes involved in sequential first-order decay reactions, and the two- step UNSATCHEM-2D code which considers equilibrium and kinetic non-equilibrium chemistry of major ions.