Hydraulic Properties Of Porous Media Research Articles

Peridynamic modeling of seepage in multiscale fractured rigid porous media

AbstractThe numerical simulation of seepage in fractured porous media holds significant relevance for subsurface energy development. The presence of fractures at various scales profoundly influences the hydraulic properties of porous media during seepage. A peridynamic (PD)‐based frame is proposed for the seepage problem analysis of multiscale fractured porous media, in which micro‐fractures are implicitly represented like the porous media, macro‐fractures are explicitly represented. For fluid flow modeling, the peridynamic bonds are divided into three types: pore seepage bond, fracture seepage bond, and fluid exchange bond. The micro‐permeabilities of different bonds are derived by Darcy's law, Poiseuille's law, and fluid exchange model, respectively. The proposed peridynamic model can naturally simulate the seepage problem of porous rock with multiscale fractures in a unified framework. Then, four cases of pore seepage and fracture seepage are analyzed using the proposed model, fractured porous media seepage with micro‐fractures and macro‐fractures are respectively considered. The predicted results are compared with the available theoretical solutions, the close agreement shows that the wide validity and applicability of the proposed model in multiscale seepage problems.

Machine learning facilitates connections between soil thermal conductivity, soil water content, and soil matric potential

Properly understanding the strongly coupled thermal and hydraulic properties of porous media is crucial to interests in different fields, e.g., agriculture, building physics and meteorology. Previous studies generally consider the thermal and hydraulic properties independently, specifically, the soil thermal conductivity curve and the soil water retention characteristics curve as methods to connect such process are unavailable or untested. In an effort to test methods based on machine learning (ML) to effectively integrate the soil thermal conductivity (λ), matric potential (ψ) and water content (θ), 2328 measurements from 43 soils were compiled using ML algorithms. Five ML algorithms, including random forest-RF, gradient boosting decision tree-GBDT, support vector machine-SVM, multiple linear regression-LR and backpropagation neural network-BPNN, based on the balanced dataset with synthetic minority over-sampling technique were trained, validated and tested to establish the λ(ψ) and λ(θ) relationships. Results demonstrate that, ML algorithms perform better than empirically based methods to optimize the thermal and hydraulic relationship. The selection of ML algorithms has a significant influence on the coupling relationship and should be taken into account. GBDT performed superior for small soil hydrothermal datasets (Testing set: Nash-Sutcliff efficiency-NSE = 0.9999 and Root Mean Square Error-RMSE = 0.0144 W m−1 K−1; independent verification: NSE = 0.7122 and RMSE = 0.2726 W m−1 K−1), while BPNN is limited by the amount of data with NSE = 0.9970, RMSE = 0.0790 W m−1 K−1 of Testing set.

Resolution-Dependent Multifractal Characteristics of Flow in Digital Rock Twin Simulated Using the Lattice Boltzmann Method

Digital rock twins are widely used to obtain hydraulic properties of porous media by simulating pore-scale fluid flow. Multifractal characteristics of pore geometry and flow velocity distribution have been discovered with two-dimensional (2D) images and three-dimensional (3D) models, whereas the dependency of results on the resolution is not well known. We investigated resolution-dependent multifractal properties of 3D twin models for a sandstone sample with originally 3 μm resolution images. 3D pore-scale water flow was simulated with the lattice Boltzmann method (LBM). As indicated by multifractal analyses, the generalized dimension spectra, the Hölder exponent spectra, and singularity spectra of the flow velocity are similar to that of the pore geometry but different in ranges and sensitivities to the change in the model resolution. Nonlinear dependencies of 2D/3D porosity, holistic/slice permeability, equivalent pore radius squared, and multifractal parameters on the resolution were discussed.

Modeling the influence of microbial growth on the hydraulic properties of porous media

Pore blocking dominates hydraulic conductivity in the processes of solute transport. Recent biological experiments have shown that the growth of microorganisms in these pores influences their hydraulic characteristics. This study proposes a microbial clogging kinetic model to examine the effects of bio-clogging based on Logistic microbial growth model. The results show that microbial clogging mainly depends on dead microbial cells rather than living microbial cells, and the contribution of dead microorganisms to microbial fouling is about 99%. The final clogging results depend on depends on the average microbial volume Vm, the maximum environmental carrying capacity K, the volume reduction coefficient of dead microorganism kd, the microbial growth rate r and the cell decomposition time Td. Compared with the experiments results, the R2 of the proposed model is exceeds 90%, which means that the model can well reflect the process of microbial clogging.

Scale dependence of tortuosity and diffusion: Finite-size scaling analysis

Physical and hydraulic properties of porous media are routinely measured/simulated at smaller scales e.g., pore and core. However, their determination at larger scales e.g., field and reservoir has still been a great challenge. Although understanding the scale dependence of transport modes in rocks and soils is essential, the porous media community still lacks in a solid theoretic framework. In this short communication, we propose finite-size scaling analysis from physics to investigate the scale dependence of tortuosity and diffusion coefficient. By comparing with two- and three-dimensional simulations, we demonstrate that the finite-size scaling analysis is a powerful approach. More specifically, we show that the plot of simulated tortuosity or diffusion coefficient versus scale looks scattered. However, after applying the finite-size scaling analysis, the data collapse together showing a quasi-universal trend.

Modeling of biofilm growth and the related changes in hydraulic properties of porous media

Pore blocking is considered to dominate the hydraulic conductivity in solute transport processes. Biomass accumulation is effective in reducing the hydraulic conductivity of porous medium. In this paper, the sphere model and the cut-and-random-rejoin-type model were adopted to establish mathematical equations for hydraulic characteristics of porous media caused by biological clogging. A new mathematical correlation was proposed to address the coupling effect of hydraulic, biofilm growth fields on the basis of thorough review on Kozeny-Carman equation relevant researches. The time-dependent solution were investigated with the consideration of a series of different model factors. The study found that there are similar phenomena both in the sphere model and in the cut-and-random-rejoin-type model. When the pores of the porous media are filled with biofilms, the pore volume is continuously reduced, and the porosity of the porous media continues to decrease. Macroscopically, it is manifested as a decrease in permeability. The model image analysis shows that growth of biofilm in a porous medium reduces the total volume and the average size of the pores and directly affects the permeability of pores. But this effect is not permanent, the pores will not be completely blocked, and the permeability will not drop to zero.

DEM-aided method for predicting the hydraulic properties with particle-size distribution of porous media

Purpose The soil water retention curve (SWRC) and unsaturated hydraulic conductivity (UHC) are crucial indices to assess hydraulic properties of porous media that primarily depend on the particle and pore size distributions. This study aims to present a method based on the discrete element model (DEM) and the typical Arya and Paris model (AP model) to numerically predict SWRC and UHC. Design/methodology/approach First, the DEM (PFC3D software) is used to construct the pore and particle size distributions in porous media. The number of particles is calculated according to the AP model, which can be applied to evaluate the relationship between the suction head and the moisture of porous media. Subsequently, combining critical path analysis (CPA) and fractal theory, the air entry value is applied to calculate the critical pore radius (CPR) and the critical volume fraction (CVF) for evaluating the unsaturated hydraulic conductivity. Findings This method is validated against the experimental results of 11 soils from the clay loam to the sand, and then the scaling parameter in the AP model and critical volume fraction value for many types of soils are presented for reference; subsequently, the gradation effect on hydraulic property of soils is analyzed. Furthermore, the calculation for unbound graded aggregate (UGA) material as a special case and a theoretical extension are provided. Originality/value The presented study provides an important insight into the relationship between the heterogeneous particle and hydraulic properties by the DEM and sheds light on the directions for future study of a method to investigate the hydraulic properties of porous media.

Hydraulic Properties of Porous Media Saturated with Nanoparticle-Stabilized Air-Water Foam

The foam generated by the mixture of air and water has a much higher viscosity and lower mobility than those of pure water or gas that constitutes the air-water foam. The possibility of using the air-water foam as a flow barrier for the purpose of groundwater and soil remediation is explored in this paper. A nanoparticle-stabilized air-water foam was fabricated by vigorously stirring the nano-fluid in pressurized condition. The foam bubble size distribution was analyzed with a microscope. The viscosities of foams generated with the solutions with several nanoparticle concentrations were measured as a function of time. The breakthrough pressure of foam-saturated microfluidic chips and sand columns were obtained. The hydraulic conductivity of a foam-filled sand column was measured after foam breakthrough. The results show that: (1) bubble coalescence and the Ostwald ripening are believed to be the reason of bubble size distribution change; (2) the viscosity of nanoparticle-stabilized foam and the breakthrough pressures decreased with time once the foam was generated; (3) the hydraulic conductivity of the foam-filled sand column was almost two orders of magnitude lower than that of a water-saturated sand column even after the foam-breakthrough. Based on the results in this study, the nanoparticle-stabilized air-water foam could be injected into contaminated soils to generate vertical barriers for temporary hydraulic conductivity reduction.

Specific surface and porosity relationship for sandstones for prediction of permeability

Porosity and specific surface are two prominent factors in describing the hydraulic properties of porous media. Determination of these two important parameters leads to identify the capability of porous media to conduct the fluids. In the present study, a new relationship between porosity and specific surface of sandstones has been developed. Micro-CT data from 10 types of sandstones has been utilized in order to present a porosity–specific surface correlation. This correlation also contains the average grain radius of each rock obtained by image processing algorithms. Finally, the correlation is tested on the provided data to evaluate its precision. The simplicity and applicability of the presented relationship can be attended to modify the Carman–Kozeny equation for sandstones.

Water Retention Curves of Biofilm‐Affected Soils using Xanthan as an Analogue

This study investigated the effect of biofilms and, in particular, that of extracellular polymeric substances (EPS) on the hydraulic properties of porous media under unsaturated conditions. The quantitative understanding of the way biological activity alters hydraulic properties is a major key in understanding and engineering relevant systems such as soil aquifer treatment, bioremediation, and wastewater irrigation. Using an EPS analog (xanthan) we explored the effect of EPS on the water retention function of two sandy soils. The result was a significant increase in the water content at any given matric head that could reach 270% of its value within pure soil. For most of the water content range, we successfully modeled the effect of the EPS as a linear superposition of the original pure soil and the xanthan retention curves. Finally, we examined two mechanisms that can attribute to modification of the water retention curve: the EPS holding capacity and alteration of the soils' pore‐size distribution; in our case, it appears that the first mechanism was dominant.

Pore‐network modeling of biofilm evolution in porous media

The influence of bacterial biomass on hydraulic properties of porous media (bioclogging) has been explored as a viable means for optimizing subsurface bioremediation and microbial enhanced oil recovery. In this study, we present a pore network simulator for modeling biofilm evolution in porous media including hydrodynamics and nutrient transport based on coupling of advection transport with Fickian diffusion and a reaction term to account for nutrient consumption. Biofilm has non-zero permeability permitting liquid flow and transport through the biofilm itself. To handle simultaneous mass transfer in both liquid and biofilm in a pore element, a dual-diffusion mass transfer model is introduced. The influence of nutrient limitation on predicted results is explored. Nutrient concentration in the network is affected by diffusion coefficient for nutrient transfer across biofilm (compared to water/water diffusion coefficient) under advection dominated transport, represented by mass transport Péclet number >1. The model correctly predicts a dependence of rate of biomass accumulation on inlet concentration. Poor network connectivity shows a significantly large reduction of permeability, for a small biomass pore volume.

Study on the selection of unsaturated flow model for the different types of soil and soft rock

Precise estimation of unsaturated hydraulic properties of porous media is indispensable in various study areas, such as analyzing the moisture flow, the drying process occurring from the surface, and the pollutant migration beneath the ground surface. Although many empirical/theoretical models describing the unsaturated hydraulic properties have been proposed by several previous researchers, the best model for the different types of soil/rock may not be identical. Thus, the model selection process and the estimation technique of the parameters included in the models should be developed. In the present study, the inverse technique based on the transient evaporation change was investigated to select the model and estimate the model parameters. The experimental work was based on a relatively low permeable soft rock and a relatively high permeable sandy soil (Toyoura standard sand). Experimental equipment was developed to precisely measure the evaporation rate for the high permeable sandy soil. The Genetic Algorithm (GA) was adopted in the inverse technique as an optimization tool. In order to simplify the problem, only the drying process from the saturated condition was considered. It was established that the information concerning the transient evaporation change could be used for the model selection and parameter estimation. Further, the saturation distribution could be used for the selection of the models. The present study provides important information for the development of the model selection process.

Soil Hydraulic Functions Determined from Measurements of Air Permeability, Capillary Modeling, and High‐Dimensional Parameter Estimation

Prediction of flow and transport through unsaturated porous media requires knowledge of the water retention and unsaturated hydraulic conductivity functions. In the past few decades many different laboratory procedures have been developed to estimate these hydraulic properties. Most of these procedures are time consuming and require significant human commitment. Furthermore, multiple measurement techniques are typically required to yield an accurate characterization of the retention and hydraulic conductivity function between full and residual saturation. We present a more efficient and robust approach to estimating the hydraulic properties of porous media. Our method derives an optimized pore‐size distribution from measurements of air permeability and using recent advances in capillary modeling and high‐dimensional parameter estimation. The section diameters of different parallel capillaries representing the pore structure of a porous medium are optimized with a multi‐algorithm optimization method by comparing measured and modeled air permeability values. The optimized pore model is subsequently used to predict the water retention and water permeability functions. The predicted soil hydraulic properties are shown to be in excellent agreement with experimentally determined data from an unconsolidated porous medium column. Our approach does not impose any functional form of the hydraulic properties and requires only measurements of air permeability.

Evaluation of the Ross fast solution of Richards’ equation in unfavourable conditions for standard finite element methods

Ross [Ross PJ. Modeling soil water and solute transport – fast, simplified numerical solutions. Agron J 2003;95:1352–61] developed a fast, simplified method for solving Richards’ equation. This non-iterative 1D approach, using Brooks and Corey [Brooks RH, Corey AT. Hydraulic properties of porous media. Hydrol. papers, Colorado St. Univ., Fort Collins; 1964] hydraulic functions, allows a significant reduction in computing time while maintaining the accuracy of the results. The first aim of this work is to confirm these results in a more extensive set of problems, including those that would lead to serious numerical difficulties for the standard numerical method. The second aim is to validate a generalisation of the Ross method to other mathematical representations of hydraulic functions. The Ross method is compared with the standard finite element model, Hydrus-1D [Simunek J, Sejna M, Van Genuchten MTh. The HYDRUS-1D and HYDRUS-2D codes for estimating unsaturated soil hydraulic and solutes transport parameters. Agron Abstr 357; 1999]. Computing time, accuracy of results and robustness of numerical schemes are monitored in 1D simulations involving different types of homogeneous soils, grids and hydrological conditions. The Ross method associated with modified Van Genuchten hydraulic functions [Vogel T, Cislerova M. On the reliability of unsaturated hydraulic conductivity calculated from the moisture retention curve. Transport Porous Media 1988;3:1–15] proves in every tested scenario to be more robust numerically, and the compromise of computing time/accuracy is seen to be particularly improved on coarse grids. Ross method run from 1.25 to 14 times faster than Hydrus-1D.

Biexponential model for water retention characteristics

Water retention characteristic (WRC) is an important soil property used in many hydrologic applications. Although there are numerous models in the literature for its prediction, the models are largely empirical with fundamental derivations based on soil textural pore-spaces. This paper presents a biexponential model for WRC that has its basis on textural and structural soil pore-spaces. The model contains physical parameters related to soil textural and structural pore characteristics and can also navigate through all inflections present in measured WRC. Thus, it adequately represents possible classes of soil pores in WRC. The performance of this model on different soil types from various parts of the world was compared to some of the popular WRC models in the literature. The models tested were those proposed by van Genuchten [van Genuchten, M.T., 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal, 44, 892–898], Campbell [Campbell, G.S., 1974. A simple method for determining unsaturated conductivity from moisture retention data. Soil Science, 117, 311–314], Brooks and Corey [Brooks, R.H., Corey, A.T., 1964. Hydraulic Properties of Porous Medium. Hydrology Paper Number 3. Colorado State University, USA.], Gardner [Gardner, W.R., 1958. Some steady state solutions of the unsaturated moisture flow equation with application to evaporation from a water table. Soil Science, 85, 228–232], Groenevelt and Grant [Groenevelt, P.H., Grant, C.D., 2004. A new model for the soil-water retention curve hat solves the problem of residual water contents. European Journal of Soil Science, 55, 479–485]. These models were found inadequate in fitting the whole range of measured WRC, are limited to certain geographic regions of the world, and contain parameters not directly linked to soil physical properties. The biexponential model does not only overcome these limitations but also gives the best fit of WRC. Its model parameters have physical significance and have been shown in this paper to be useful in fitting different soil physical conditions. The model is continuous and continuously differentiable throughout the whole range of WRC and is envisaged to perform equally well in fitting unsaturated hydraulic conductivity.

Systematic study of steam–water capillary pressure

Although steam–water capillary pressure is of central importance in geothermal reservoir engineering, it is nevertheless still poorly understood because of the difficulties involved in making direct measurements. To this end, we have conducted some experimental and theoretical studies. Unique methods have been developed to measure capillary pressures in order to overcome the complications in laboratory procedures associated with mass transfer as temperature and pressure changes. Both steam–water and air–water capillary pressures were measured and compared. Significant differences were found; in the cases studied, the steam–water capillary pressures were smaller. The drainage capillary pressure was greater than the imbibition capillary pressure, as was expected. Using experimental data, an empirical model was derived to calculate steam-water capillary pressure directly. Also developed was a generalized capillary pressure model based on fractal modeling of a porous medium; it encompasses the frequently used Brooks–Corey model (Brooks, R.H., Corey, A.T., 1964. Hydraulic Properties of Porous Media. Colorado State University, Hydro paper No. 3, Fort Collins, CO, USA, 24 pp.) as well as others. Recent studies on the topic are summarized and reviewed.

Free‐form estimation of the unsaturated soil hydraulic properties by inverse modeling using global optimization

Inverse modeling is a powerful technique for identifying the hydraulic properties of unsaturated porous media. However, the selection of an appropriate parameterization of the soil water retention and hydraulic conductivity function remains a challenge. In this article, we present an improved algorithm for estimating these two relationships without assigning an a priori shape to them. The approach uses cubic Hermite interpolation and a global optimization strategy. A multilevel routine identifies the adequate number of degrees of freedom by balancing model performance, the statistical interaction of the estimated model parameters, and their number. A first‐order uncertainty analysis provides a quantitative measure of how well the soil hydraulic properties can be identified in different ranges of pressure head. This offers great potential for designing optimal experimental procedures for identifying the hydraulic properties of porous media. We demonstrate the effectiveness of the algorithm for the evaluation of multistep outflow experiments by investigating synthetic data sets and real measurements. The free‐form approach yields optimal model parameters that show only moderate correlation, indicating well‐posed inverse problems. Since parameterization errors are almost completely avoided, the algorithm is well suited to identifying other error sources in unsaturated flow problems, e.g., limitations in the applicability of the Richards equation or problems caused by spatial heterogeneity.

Analysis of solute transport in a divergent flow tracer test with scale‐dependent dispersion

AbstractIt has been known for many years that dispersivities increase with solute displacement distance in a subsurface. The increase of dispersivities with solute travel distance results from significant variation in hydraulic properties of porous media and was identified in the literature as scale‐dependent dispersion. In this study, Laplace‐transformed analytical solutions to advection‐dispersion equations in cylindrical coordinates are derived for interpreting a divergent flow tracer test with a constant dispersivity and with a linear scale‐dependent dispersivity. Breakthrough curves obtained using the scale‐dependent dispersivity model are compared to breakthrough curves obtained from the constant dispersivity model to illustrate the salient features of scale‐dependent dispersion in a divergent flow tracer test. The analytical results reveal that the breakthrough curves at the specific location for the constant dispersivity model can produce the same shape as those from the scale‐dependent dispersivity model. This correspondence in curve shape between these two models occurs when the local dispersivity at an observation well in the scale‐dependent dispersivity model is 1·3 times greater than the constant dispersivity in the constant dispersivity model. To confirm this finding, a set of previously reported data is interpreted using both the scale‐dependent dispersivity model and the constant dispersivity model to distinguish the differences in scale dependence of estimated dispersivity from these two models. The analytical result reveals that previously reported dispersivity/distance ratios from the constant dispersivity model should be revised by multiplying these values by a factor of 1·3 for the scale‐dependent dispersion model if the dispersion process is more accurately characterized by scale‐dependent dispersion. Copyright © 2007 John Wiley & Sons, Ltd.

Assessment of an efficient numerical solution of the 1D Richards' equation on bare soil

A new numerical scheme has been proposed by Ross [Ross, P.J., 2003. Modeling soil water and solute transport—fast, simplified numerical solutions. Agronomy Journal 95, 1352–1361] to solve the 1D Richards' equation [Richards, L.A., 1931. Capillary conduction of liquids through porous medium. Physics 1, 318–333]. This non-iterative solution uses the description of soil properties proposed by Brooks and Corey [Brooks, R.H., Corey, A.T., 1964. Hydraulic properties of porous media. Colorado State University, Fort Collins]. It allows the derivation of an analytical expression for the Kirchhoff potential used in the calculation of water fluxes. The degree of saturation is used as the dependent variable when the soil is unsaturated and the Kirchhoff potential is used in case of saturation. A space and time discretisation scheme leads to a tridiagonal set of linear equations that is solved non-iteratively. We propose in this paper an extensive test of this numerical method, evaluated only on a single case by Ross. The tests are conducted in two steps. First, the solution is assessed against two analytical solutions. The first one [Basha, H.A., 1999. Multidimensional linearized nonsteady infiltration with prescribed boundary conditions at the soil surface. Water Resources Research 35(1), 75–93] provides the water content profile when simplified soil characteristics such as the exponential law of Gardner [Gardner, W.R., 1958. Some steady-state solutions of the unsaturated moisture flow equations with application to evaporation from a water table. Soil Science 85, 228–232] are used. The Ross solution is compared to this solution on eight different soils that were fitted to this law. Analytical solution with the Brooks and Corey models is not available at the moment for the moisture profile but some exist for cumulative infiltration. Therefore, the second analytical solution, used in this study, is the one developed by Parlange et al. [Parlange, J.-Y., Haverkamp, R., Touma, J., 1985. Infiltration under ponded conditions: 1. Optimal analytical solution and comparison with experimental observations. Soil Science 139(4), 305–311] and Haverkamp et al. [Haverkamp, R., Parlange, J.-Y., Starr, J.L., Schmitz, G., Fuentes, C., 1990. Infiltration under ponded conditions: 3. A predictive equation based on physical parameters. Soil Science 149(5), 292–300]. The various parameters of this solution are written for the Brooks and Corey models and the cumulative infiltration calculated by the Ross solution is compared to this analytical solution. The second part of the test is a comparison with a reference model: the SiSPAT (Simple Soil Plant Atmosphere Transfer) model, which provides a reference iterative solution of the soil water flow equation. A wide range of simulations is performed, with various soil types (homogeneous or not), various climate forcing and several initial conditions. It allows the comparison of various variables such as deep drainage, soil moisture profile, surface ponding, and evaporation under non-uniform initial moisture content and time varying climate forcing. We show that the model provides robust and accurate solutions as compared with the analytical solutions and with the SiSPAT model. This study also shows that a finer discretization than the one proposed by Ross is necessary close to the soil surface to accurately model the cumulative infiltration, especially for clayey soils.

Measurement of Hydraulic Characteristics of Porous Media Used to Grow Plants in Microgravity

Understanding the effect of gravity on hydraulic properties of plant growth medium is essential for growing plants in space. The suitability of existing models to simulate hydraulic properties of porous medium is uncertain due to limited understanding of fundamental mechanisms controlling water and air transport in microgravity. The objective of this research was to characterize saturated and unsaturated hydraulic conductivity (K) of two particle-size distributions of baked ceramic aggregate using direct measurement techniques compatible with microgravity. Steady state (Method A) and instantaneous profile measurement (Method B) methods for K were used in a single experimental unit with horizontal flow through thin sections of porous medium providing an earth-based analog to microgravity. Comparison between methods was conducted using a crossover experimental design compatible with limited resources of space flight. Satiated (natural saturation) K ranged from 0.09 to 0.12 cm s-1 and 0.5 to >1 cm s-1 for 0.25- to 1- and 1- to 2-mm media, respectively. The K at the interaggregate/intraaggregate transition was approximately 10(-4) cm s-1 for both particle-size distributions. Significant differences in log(10)K due to method and porous medium were less than one order of magnitude and were attributed to variability in air entrapment. The van Genuchten/Mualem parametric models provided an adequate prediction of K of the interaggregate pore space, using residual water content for that pore space. The instantaneous profile method covers the range of water contents relevant to plant growth using fewer resources than Method A, all advantages for space flight where mass, volume, and astronaut time are limited.