Search

Highlights • Estimation of heterogeneous hydraulic conductivity and van Genuchten α and n fields • Iterative EnKF successfully estimated jointly the soil parameter fields. • In the 3D-case, soil parameter estimation is less improved than for 2D-case. • 1D parameter estimation at measurement locations plus kriging performs as good as 3D-IEnKF. Abstract The accurate modeling of flow and transport in the vadose zone for agricultural and environmental applications requires knowledge about soil parameters. Soil parameters vary in space depending on soil texture and structure. In the present synthetic study we considered spatial variation of permeability (k), inverse of capillary entry pressure head (α VG) and exponent (n) of the Mualem-van Genuchten model. The iterative Ensemble Kalman filter (IEnKF) can estimate the spatially variable soil parameters if measurements of water saturation at different locations and times are available. We used as input daily precipitation data from the Berambadi catchment (southern India). We first considered that the parameters vary horizontally but are constant in the vertical direction. In this case log (k) and log (α VG) can be estimated satisfactorily with 30%–40% reduction of RMSE (compared to open loop runs), if the initial guess of the spatial correlation lengths of the heterogeneous fields is equal to or larger than the unknown, true values. The estimation of exponent n is poorer as the reduction of RMSE is just 20%. If vertical heterogeneity of the parameters is considered the estimation of log (k) and log (α VG) is only improved for the upper 1.5 m and estimation of n is not improved. We also demonstrate that the estimation problem can be simplified when flow in the unsaturated zone is predominantly vertical. If in this case soil hydraulic parameters are estimated with IEnKF at measurement locations and afterwards interpolated with kriging, results are produced with a similar quality as with 3D-IEnKF. [ABSTRACT FROM AUTHOR]

We explore how X-ray computed microtomography can be used to generate highly-resolved 3D biofilm datasets on length scales that span multiple pore bodies. The data is integrated into a study of the effects of flow rate on three-dimensional growth of biofilm in porous media. Three flow rates were investigated in model packed-bed columns. Biofilm growth was monitored during an 11-day growth period using a combination of differential pressure and effluent dissolved oxygen measurements. At the end of the growth period, all columns were scanned using X-ray computed microtomography and a barium sulfate-based contrast agent. The resulting images were prepared for quantitative analysis using a novel image processing workflow that was tailored to this specific system. The reduction in permeability due to biofilm growth was studied using both transducer-based pressure drop measurements and image-based calculations using the Kozeny–Carman model. In addition, a set of structural measures related to the spatial distribution of biofilms were computed and analyzed for the different flow rates. We generally observed 1 to 2 orders of magnitude decrease in permeability as a result of bioclogging for all columns (i.e, across flow rates). The greatest average permeability and porosity reduction was observed for the intermediate flow rate (4.5 ml/h). A combination of results from different measurements all suggest that biofilm growth was oxygen limited at the lowest flow rate, and affected by shear stresses at the highest flow rate. We hypothesize that the interplay between these two factors drives the spatial distribution and quantity of biofilm growth in the class of porous media studied here. Our approach opens the way to more systematic studies of the structure-function relationships involved in biofilm growth in porous media and the impact that such growth may have on physical properties such as hydraulic conductivity. [ABSTRACT FROM AUTHOR]

Knowledge of sub-core permeability is necessary for accurate numerical modeling of coreflooding experiments and for investigation of sub-core flow phenomenon. A new method for estimating sub-core permeability geometric mean ( k G ) and log-permeability variance ( σ y 2 ) is presented. The method is based on matching coreflooding experiment measurements of wetting phase relative permeability with semi-analytical calculations of effective relative permeability. The semi-analytical solution is formulated assuming log-normal permeability ( k ), steady state and capillary-limit conditions. It is based on the geometric mean and log-phase-permeability variance for isotropic k and power law averaging for anisotropic correlations. The solution is validated on synthetic k realizations by comparison with numerical calculations. Then, the estimation method is tested on synthetic data assuming various types of core capillary pressure relationships, relative permeability functions and k anisotropies. Results demonstrate high accuracy in almost all of the cases except for small anisotropy ratios l h / l v between horizontal ( l h ) and vertical ( l v ) dimensionless correlation lengths, where flow is in the horizontal direction, and when σ y 2 is large. The method is also validated using data from CO 2 -brine coreflooding experiments conducted on two different cores. It is found that the estimation method remains accurate in these realistic settings, however, accuracy of k G is reduced when the core permeability departs from a log-normal distribution. [ABSTRACT FROM AUTHOR]

Pore-network models were found useful in describing important flow and transport mechanisms and in predicting flow properties of different porous media relevant to numerous fundamental and industrial applications. Pore-networks provide very fast computational framework and permit simulations on large volumes of pores. This is possible due to significant pore space simplifications and linear/exponential relationships between effective properties and geometrical characteristics of the pore elements. To make such relationships work, pore-network elements are usually simplified by circular, triangular, square and other basic shapes. However, such assumptions result in inaccurate prediction of transport properties. In this paper, we propose that pore-networks can be constructed without pore shape simplifications. To test this hypothesize we extracted 3292 2D pore element cross-sections from 3D X-ray microtomography images of sandstone and carbonate rock samples. Based on the circularity, convexity and elongation of each pore element we trained neural networks to predict the dimensionless hydraulic conductance. The optimal neural network provides 90% of predictions lying within the 20% error bounds compared against direct numerical simulation results. Our novel approach opens a new way to parameterize pore-networks and we outlined future improvements to create a new class of pore-network models without pore shape simplifications. [ABSTRACT FROM AUTHOR]

The goal of this study is to evaluate the conductivity of random close packings of non-spherical, rod-shaped proppant particles under the closure stress using numerical simulation and lab tests, with application to the conductivity of hydraulic fractures created in subterranean formation to stimulate production from oil and gas reservoirs. Numerical simulations of a steady viscous flow through proppant packs are carried out using the lattice Boltzmann method for the Darcy flow regime. The particle packings were generated numerically using the sequential deposition method. The simulations are conducted for packings of spheres, ellipsoids, cylinders, and mixtures of spheres with cylinders at various volumetric concentrations. It is demonstrated that cylinders provide the highest permeability among the proppants studied. The dependence of the nondimensional permeability (scaled by the equivalent particle radius squared) on porosity obtained numerically is well approximated by the power-law function: K / R v 2 = 0.204 ϕ 4.58 in a wide range of porosity: 0.3 ≤ ϕ ≤ 0.7. Lattice-Boltzmann simulations are cross-verified against finite-volume simulations using Navier–Stokes equations for inertial flow regime. Correlations for the normalized beta-factor as a function of porosity and normalized permeability are presented as well. These formulae are in a good agreement with the experimental measurements (including packings of rod-shaped particles) and existing laboratory data, available in the porosity range 0.3 ≤ ϕ ≤ 0.5. Comparison with correlations by other authors is also given. [ABSTRACT FROM AUTHOR]

A common way to simulate fluid flow in porous media is to use Lattice Boltzmann (LB) methods. Permeability predictions from such flow simulations are controlled by parameters whose settings must be calibrated in order to produce realistic modelling results. Herein we focus on the simplest and most commonly used implementation of the LB method: the single-relaxation-time BGK model. A key parameter in the BGK model is the relaxation time τ which controls flow velocity and has a substantial influence on the permeability calculation. Currently there is no rigorous scheme to calibrate its value for models of real media. We show that the standard method of calibration, by matching the flow profile of the analytic Hagen-Poiseuille pipe-flow model, results in a BGK-LB model that is unable to accurately predict permeability even in simple realistic porous media (herein, Fontainebleau sandstone). In order to reconcile the differences between predicted permeability and experimental data, we propose a method to calibrate τ using an enhanced Transitional Markov Chain Monte Carlo method, which is suitable for parallel computer architectures. We also propose a porosity-dependent τ calibration that provides an excellent fit to experimental data and which creates an empirical model that can be used to choose τ for new samples of known porosity. Our Bayesian framework thus provides robust predictions of permeability of realistic porous media, herein demonstrated on the BGK-LB model, and should therefore replace the standard pipe-flow based methods of calibration for more complex media. The calibration methodology can also be extended to more advanced LB methods. [ABSTRACT FROM AUTHOR]

To consider the non-Darcian nature of groundwater flow and the permeability reduction owing to well and aquifer clogging, an Izbash's law-based analytical model with a time-dependent hydraulic conductivity function is proposed for constant-rate recharge and constant-head recharge. By means of linearization approximations, variable substitutions and the Laplace transform, approximate analytical solutions for the model are derived. Comparison of developed approximate analytical solutions with numerical solutions indicates that the approximate solutions are highly accurate except during the short period of initial recharge stage. The proposed model provides a theoretical basis for managed aquifer recharge involving clogging-related permeability reduction and non-Darcian flow. [ABSTRACT FROM AUTHOR]

• Steady source flow in aquifer of lognormal permeability. • The equivalent conductivity K eq quantifies heterogeneity. • The dependence of Keq on distance and properties is determined. • K eq tends rapidly to the effective conductivity in uniform flow. • K eq expression can be conveniently used in the inversion of hydraulic tomography data. The effective conductivity of heterogeneous aquifers K efu relates the mean flux to the mean head gradient in mean uniform (natural gradient) flow. While K efu depends on the hydraulic conductivity K statistical moments (K G , the geometric mean and σ Y 2 , the logconductivity variance for a given structure model) it is not a local property for strongly nonuniform well flow. In hydraulic tomography, flow to a short well segment which is considered here, can be approximated by that toward a source in a three-dimensional heterogeneous medium. We investigate the equivalent conductivity K eq , which unlike K efu , is a measurable property, directly related to the head H (or its mean) and the discharge. The dependence of K eq on K statistics and distance r from the source is determined for steady source flow in a formation of random stationary and statistically isotropic K. For the first time K eq is derived by numerical simulations for σ Y 2 ≤ 4. The derivation of the transition of K eq from the local exact value for r / I << 1 (I is the integral scale) to K efu for r / I ⪆1 is one of the main results of the study. Application to a synthetic example of hydraulic tomography to derive K G , σ Y 2 and I , from H measurements, demonstrates the promise of the method and calls for its further development and validation. [ABSTRACT FROM AUTHOR]

• Flume experiments and numerical models of solute transport in a layered bedform were conducted. • A combination of mechanisms produces irregular spatial patterns of solute transport in the hyporheic zone. • Disconnected transportation was formed under a discontinuous low-permeability layer. Hyporheic exchange is affected by bedform geometry, which induces complex flow paths within the bedform. Additional factors that influence flow and solute transport in the hyporheic zone are layered profile sediments and density-driven flow. This study explored the combined effects of these factors on hyporheic exchange through laboratory experiments and numerical simulations involving infiltrating solute displacing less-dense resident water in a layered bedform with a low permeability layer (LPL). The bedform consisted of three horizontal layers, in which the hydraulic conductivity of the middle layer (LPL) was less than that of the top (TL) and bottom layers (BL). The results demonstrated that a previously unexplored combination of mechanisms (density effects and layered bedform) produces irregular spatial patterns of solute transport in the hyporheic zone. For instance, the width of solute plume within the bottom layers becomes narrowed compared with tracer transport. With increasing density contrast between infiltrating solute and resident water, the solute plume becomes much narrower, forming fingers. Numerical modeling further shows that the hydraulic conductivity contrast (HCC) and relative thickness (RT) of the hyporheic zone layers also affect the spatial solute transport patterns. As the hydraulic conductivity contrast or relative thickness increases, the plume becomes much narrower. Horizontal ambient flow (HAF) dominated in the bottom layers, and lateral solute spreading and mixing intensified with a higher hydraulic conductivity contrast and relative thickness. Furthermore, the vertical solute plume was detached by the horizontal ambient flow in the bottom layers with a discontinuous low permeability layer, forming a discontinuous zone of vertical solute transport. Image, graphical abstract [ABSTRACT FROM AUTHOR]

• An effective porosity approach was proposed for describing permeability variation during microbially induced calcite precipitation. • The performance of using different porosity-permeability relationships to simulate the permeability change during microbially induced calcite precipitation has been discussed. • The predictive ability of the model has been estimated through simulations of laboratory tests under different treatment strategies. • The effects of the reaction rate on the spatial and temporal evolution of the precipitated calcite were analyzed. Microbially induced calcite precipitation (MICP) provides the potential for developing innovative and environmentally friendly techniques to improve the engineering properties of soil through reduction of permeability in soil and increase of soil stiffness and strength. In the present research work, coupled bio-chemo-hydraulic modelling was developed to enhance the understanding of the coupled processes involved in MICP and to predict the MICP performance in permeability reduction. In the model, an overall kinetically controlled model is adopted to describe the biochemical reactions, where the reaction rate is dependent on the concentration of both bacteria and chemical reactants. Specifically, an effective porosity concept was proposed and implemented in the model to capture the effects of pore throat blockage on permeability reduction caused by precipitated calcite. Correspondingly, the Kozeny-Carman equation was modified to describe the permeability variation during MICP. This model has been applied to simulate two laboratory experiments. The observed changes in chemical components and hydraulic conductivity can be well reproduced in the model. Through comparisons of the effective porosity concept to other commonly used porosity-permeability relationships, it is estimated that effective porosity should be considered to simulate the permeability reduction observed in MICP. Furthermore, a sensitivity analysis of the reaction-related parameters was conducted. The results of the sensitivity analysis indicate that the maximum urease rate has a strong influence on the biochemical hydraulic responses in MICP. [ABSTRACT FROM AUTHOR]