Modeling microbial processes in porous media

 The incorporation of microbial processes into reactive transport models has generally proceeded along two separate lines of investigation: (1) transport of bacteria as inert colloids in porous media, and (2) the biodegradation of dissolved contaminants by a stationary phase of bacteria. Research over the last decade has indicated that these processes are closely linked. This linkage may occur when a change in metabolic activity alters the attachment/detachment rates of bacteria to surfaces, either promoting or retarding bacterial transport in a groundwater-contaminant plume. Changes in metabolic activity, in turn, are controlled by the time of exposure of the microbes to electron acceptors/donor and other components affecting activity. Similarly, metabolic activity can affect the reversibility of attachment, depending on the residence time of active microbes. Thus, improvements in quantitative analysis of active subsurface biota necessitate direct linkages between substrate availability, metabolic activity, growth, and attachment/detachment rates. This linkage requires both a detailed understanding of the biological processes and robust quantitative representations of these processes that can be tested experimentally. This paper presents an overview of current approaches used to represent physicochemical and biological processes in porous media, along with new conceptual approaches that link metabolic activity with partitioning of the microorganism between the aqueous and solid phases. Received, January 1999 · Revised, June 1999, July 1999 · Accepted, October 1999     

Modeling of dynamic cohesive fracture propagation in porous saturated media

In this paper, a mathematical model is presented for the analysis of dynamic fracture propagation in the saturated porous media. The solid behavior incorporates a discrete cohesive fracture model, coupled with the flow in porous media through the fracture network. The double‐nodded zero‐thickness cohesive interface element is employed for the mixed mode fracture behavior in tension and contact behavior in compression. The crack is automatically detected and propagated perpendicular to the maximum effective stress. The spatial discretization is continuously updated during the crack propagation. Numerical examples from the hydraulic fracturing test and the concrete gravity dam show the capability of the model to simulate dynamic fracture propagation. The comparison is performed between the quasi‐static and fully dynamic solutions, and the performance of two analyses is investigated on the values of crack length and crack mouth opening. Copyright © 2010 John Wiley & Sons, Ltd.     

Modeling compositional compressible two-phase flow in porous media by the concept of the global pressure

We derive a new formulation for the compositional compressible two-phase flow in porous media. We consider a liquid–gas system with two components: water and hydrogen. The formulation considers gravity, capillary effects, and diffusivity of each component. The main feature of this formulation is the introduction of the global pressure variable that partially decouples the system equations. To formulate the final system, and in order to avoid primary unknowns changing between one-phase and two-phase zones, a second persistent variable is introduced: the total hydrogen mass density. The derived system is written in terms of the global pressure and the total hydrogen mass density. The system is capable of modeling the flows in both one and two-phase zones with no changes of the primary unknowns. The mathematical structure is well defined: the system consists of two nonlinear parabolic equations, the global pressure equation, and the total hydrogen mass density equation. The derived formulation is fully equivalent to the original one. Numerical simulations show ability of this new formulation to model efficiently the phase appearance and disappearance.     

Accurate and stablised time integration strategy for saturated porous media dynamics

Acta Geotechnica - When applying equal-order monolithic schemes for the solution of incompressible fluid saturated porous media dynamics, the resulting pressure field often exhibit spurious...     

Modeling cohesive fracture propagation in partially saturated porous media with the assumed enhanced strain method

Acta Geotechnica - The assumed enhanced strain (AES) method is developed to simulate cohesive fracture propagation in the partially saturated porous media which includes the solid skeleton and the...     

Dynamics of MTBE-degrading activity in porous media using a large-scale laboratory experiment

Methyl tert-butyl ether (MTBE) is an oxygenated organic compound that tends to form large groundwater contamination plumes. If bioaugmentation is used as a remediation technique, the question of the mobility of the bioactive zone (BAZ) with time is of interest. The objective of this experiment was to study the spatial redistribution of MTBE-biodegradation activity through time, following the injection of a bacterial culture in a homogeneous porous media, at high pressures and concentrations. The experiment was performed using a large-scale aquifer physical model, which can incorporate physicochemical heterogeneities similar to those found in the field, under controlled laboratory conditions. The experimental tank was filled with 1.0-mm-diameter glass beads to represent a homogeneous high hydraulic conductivity porous medium. During inoculation, the bacterial culture was distributed in a circular pattern. Initially it appeared that the BAZ was located in the upstream portion of the inoculated zone, where oxygen was available in conjunction with the inoculated bacteria and MTBE. With time, the BAZ moved upgradient through the whole tank towards the inlet. This implies the successful movement of bacteria from the inoculation area against advective flow into previously sterile zones of the tank. A mass balance showed that dissolved oxygen concentrations were likely not a limiting factor during the experiments.     

Modeling of subsidence and stress-dependent hydraulic conductivity for intact and fractured porous media

Summary This study investigates the changes in deformation and stress dependent hydraulic conductivities that occur as a result of underground mining in intact and fractured porous media. The intact porous medium is assumed to be comprised of regularly packed spherical grains of uniform size. The variation in grain size or pore space due to the effect of changing intergranular stresses results in a change in rock hydraulic conductivity. A model is developed to describe the sensitivity of hydraulic conductivity to effective stresses through Hertzian contact of spherical grains. The fractured porous medium is approximated as an equivalent fracture network in which a single fracture is idealized as a planar opening having a constant equivalent thickness or aperture. Changes in fracture aperture as a result of changes in elastic deformation control the variation of hydraulic conductivity. A model is presented to illustrate the coupling between strain and hydraulic conductivity. Subsidence induced deformations that result from mining induced changes in hydraulic conductivity in both intact and fractured media. These changes are examined and compared with results from a mining case study.     

Modeling of chemo-hydromechanical behavior of unsaturated porous media: a nonlocal approach based on integral equations

Acta Geotechnica - Unsaturated clay is a heterogeneous porous medium consisting of three phases, namely solid soil skeleton, pore water, and pore air. It has been well recognized that the variation...     

Modeling permeability in imperfectly layered porous media. II. A two-dimensional application of block-scale permeability

In the previous paper (Zijl and Stam, 1992), a theory has been developed to calculate the nine components of the three-dimensional intrinsic permeability tensor on the scale of a grid-block from a local-scale, predominantly layered subsurface. The resulting block-scale expressions can be written as a perturbation series of which the first term, or zeroth-order solution, coincides with the conventionally applied arithmetic and harmonic averages over the layers of the subsurface. The derived expressions permit the calculation of the diagonal and off-diagonal terms of the permeability tensor. In the present paper, these expressions will be applied in some numerical examples. Two basic two-dimensional hypothetical permeability distributions are adopted, and the various terms of the theoretical expressions are calculated. The results will be used to derive guidelines to discern the situations where higher order solutions can be neglected, and where conventional harmonic and arithmetic averages give a good estimate of the permeability on grid-block scale.     

Crack nucleation in saturated porous media

Crack nucleation has been the subject of important contributions in the last two last decades. However, it seems that few attention has been granted to the case of saturated porous media. This is the question addressed in the present paper which is devoted to nucleation in traction mode. From a physical point of view, nucleation is a sudden phenomenon, so that the material response is both adiabatic and undrained. In the spirit of the variational approach, the nucleated crack is viewed as the final state of a region of space in which the material undergoes a full damage process. In traction mode, the opening of a saturated crack in undrained condition induces a drop of fluid pressure. In case of low fluid compressibility, the presence of the fluid delays the brittle failure usually associated with nucleation, as long as the fluid pressure remains above the saturation vapor pressure. Nucleation is therefore possible only if a partial vaporization of the fluid takes place.     

Experimental investigations on the formation of excess air in quasi-saturated porous media

The formation of an excess of dissolved gas (“excess air”) in quasi-saturated media was studied by analyzing and interpreting dissolved noble gas concentrations in laboratory column experiments. Using quartz sand filled columns of 1 m length, two different experimental designs were realized. In the first, groundwater recharge was simulated by a unidirectional vertical water flow through the columns. In the second, groundwater level fluctuations in an aquifer zone without active infiltration were reproduced by cyclic water level fluctuations in the columns. The reproducible generation of excess air under these defined, near natural conditions was successful. Partial or complete dissolution of air bubbles entrapped in the quartz sand could be identified as the mechanism responsible for the generation of excess air. Depending on the experimental design, supersaturation of the dissolved atmospheric noble gases ranging between 1.4% ΔNe and 16.2% ΔNe was found. The measured noble gas patterns were interpreted using inverse modeling and conceptual gas exchange models and were compared to results of numerical simulations of gas bubble dissolution in water filled soil columns. The gas composition in most of the samples resembles either unfractionated pure atmospheric excess air or is fractionated in accordance with closed-system equilibration between entrapped air and surrounding water. In addition to the amount of entrapped air, the hydrostatic pressure exerted on the entrapped air bubbles is the dominating parameter responsible for the total amount of dissolved air. The composition of the excess air component is controlled by the water flow regime, the bubble size distribution, the initially dissolved gas concentrations and the initially entrapped gas composition.     

Weak discontinuity in porous media: an enriched EFG method for fully coupled layered porous media

In this paper, a series of multimaterial benchmark problems in saturated and partially saturated two‐phase and three‐phase deforming porous media are addressed. To solve the process of fluid flow in partially saturated porous media, a fully coupled three‐phase formulation is developed on the basis of available experimental relations for updating saturation and permeabilities during the analysis. The well‐known element free Galerkin mesh‐free method is adopted. The partition of unity property of MLS shape functions allows for the field variables to be extrinsically enriched by appropriate functions that introduce existing discontinuities in the solution field. Enrichment of the main unknowns including solid displacement, water phase pressure, and gas phase pressure are accounted for, and a suitable enrichment strategy for different discontinuity types are discussed. In the case of weak discontinuity, the enrichment technique previously used by Krongauz and Belytschko [Int. J. Numer. Meth. Engng., 1998; 41:1215–1233] is selected. As these functions possess discontinuity in their first derivatives, they can be used for modeling material interfaces, generating only minor oscillations in derivative fields (strain and pressure gradients for multiphase porous media), as opposed to unenriched and constrained mesh‐free methods. Different problems of multimaterial poro‐elasticity including fully saturated, partially saturated one, and two‐phase flows under the assumption of fully coupled extended formulation of Biot are examined. As a further development, problems involved with both material interface and impermeable discontinuities, where no fluid exchange is permitted across the discontinuity, are considered and numerically discussed. Copyright © 2014 John Wiley & Sons, Ltd.     

悬浮微小颗粒对多孔介质渗流特性影响的实验研究

在清洁水渗流实验的基础上,开展了恒水头条件下不同浓度的含悬浮颗粒流体在多种填充粒径的多孔介质内的渗流实验。结果表明:悬浮颗粒在多孔介质段的沉积,并不一定使多孔介质局部相对渗透系数(k_t/k_0)降低,相反在一定情况下会出现局部相对渗透系数增大的情况。较小悬浮颗粒浓度下,悬浮颗粒粒径越小,曲线波峰出现越迟,相对渗透系数增加幅度越大;而较大进口浓度则抑制(k_t/k_0)曲线波峰的生成,直至相对渗透系数单调递减。通过包括前人实验数据在内的悬浮颗粒浓度C_0与颗粒直径比值d_p/D_p(悬浮颗粒直径/多孔介质颗粒直径)有无相对渗透系数增加现象的对照图,进一步揭示了含悬浮颗粒流体在多孔介质内的运移与沉积规律。     

多孔介质中气泡尺寸对流动阻力的影响

多孔介质中的泡沫能够封堵某些孔道,降低气体流动性。由于直接观察多孔介质中的泡沫流动比较困难,所以关于泡沫流动性与气泡尺寸之间的关系研究较少。利用Navier-Stokes方程与守恒的水平集方法耦合模拟孔隙介质中气泡尺寸对流动阻力的影响,结果证实,气泡尺寸是影响流体阻力的重要因素。当气泡半径小于孔喉半径时,气泡不受孔道约束,气泡流动过程中流动阻力较稳定,此时含气泡流体流动阻力与纯液态流体流动阻力相等,所以小于孔喉尺寸的气泡对孔道无封堵作用。当气泡半径大于孔喉半径时,孔道影响气泡变形,其流动阻力存在波动性,最大流动阻力随气泡体积变大呈线性增加。当气泡体积增加到使最大流动阻力达极大值时,继续增大气泡体积,最大流动阻力随气泡体积增大而线性降低。最大流动阻力随气泡体积增大而线性增大与减小变化具有周期性,周期为单位孔体体积。     

A numerical study on the impact of thermal alterations in porous media during hot fluid injection process employing a modified Boussinesq model

The Oberbeck-Boussinesq (OB) approximation is widely employed as a simplifying assumption for density-dependent flow problems. It reduces the governing differential equations to simpler forms, which can be handled analytically or numerically. In this study, a modified OB model is formulated to account for the variation of rock permeability and porosity with temperature during the hot fluid injection process in an oil-saturated porous medium under the assumption of local thermal equilibrium (LTE). The mathematical model is solved numerically using a fully implicit control volume finite difference discretization with the successive over relaxation (SOR) method to handle the non-linearity. Subsequently, the numerical model is validated with the analytical solution of the simplified problem successfully. Through detailed sensitivity analyses, the simulation results reveal the hot fluid injection rate as the most important operational parameter to be optimized for a successful thermal flood. The numerical runs show that that for single-phase core-flood simulation, the effect of temperature on the rock absolute permeability and porosity can be neglected without introducing any significant errors in the estimated recovery and temperature profile.     

Modeling permeability in imperfectly layered porous media. I. Derivation of block-scale permeability tensor for thin grid-blocks

Practical expressions are given for the nine components of the block-scale permeability tensor of a thin block. These expressions are derived from the local-scale continuity equation and Darcy's law in an anisotropic layered porous medium. The flow problem is separated in a bottom-flux problem and a top-flux problem, both of which can be solved in essentially the same way. The bottom-flux problem has been worked out in detail, and has been separated in two parts: a vertical potential difference and a horizontal potential difference part. Each is solved with a different approach specially designed for it. Depth-averaged expressions are obtained first, after which block-scale expressions are obtained by assuming a constant depth-averaged flux. In the zeroth order, this results in the well-known Dupuit approximation in geohydrology, and the vertical equilibrium (VE) approximation in petroleum reservoir engineering. The novelty of the theory presented here stems from the application of a perturbation technique to obtain first-order corrections to these well-known results. The local-scale laws are applied in the coordinate system coinciding with the principal axes of the local-scale permeability tensor. Only in this coordinate system the local-scale permeability tensor has zero off-diagonal components. However, since the porous medium is imperfectly layered, the first-order corrections show that the off-diagonal components of the block-scale permeability tensor are not zero. Furthermore, the block-scale permeability tensor is generally nonsymmetric, which implies that a coordinate system in which the off-diagonal terms disappear does not exist.     

Dynamic capillary effects in heterogeneous porous media

In standard multi-phase flow models on porous media, a capillary pressure saturation relationship developed under static conditions is assumed. Recent experiments have shown that this static relationship cannot explain dynamic effects as seen for example in outflow experiments. In this paper, we use a static capillary pressure model and a dynamic capillary pressure model based on the concept of Hassanizadeh and Gray and examine the behavior with respect to material interfaces. We introduce a new numerical scheme for the one-dimensional case using a Lagrange multiplier approach and develop a suitable interface condition. The behavior at the interface is discussed and verified by various numerical simulations.     

Bioclogging in porous media under continuous-flow condition

Bioclogging extensively exists in porous media, such as permeable reactive barrier, constructed wetland, reverse osmosis, and biofilter systems. Microorganisms overproduce and affect the efficiency of sewage treatment. In this paper, variations in biochemical and hydraulic parameters during the clogging process were obtained using various column experiments. The hydraulic conductivity first decreased sharply to 18.32 % of the original value at the 12th day and decreased to 2.71 % at the end of the experiment, a reduction of more than an order of magnitude. The hydrodynamic dispersion had the highest increase at 7.13 times the initial value and ultimately decreased to 29 %. The porosity decreased to 47.24 % of the initial value, and the total bacterial count in the inlet of the column increased from 3.4 × 10⁶ to 8.8 × 10⁸ cells/mL. Based on the biochemical and hydraulic parameter variation, the clogging process can be divided into four stages: (1) severe clogging occurs, and aerobic microorganisms reproduce rapidly in the inlet; (2) clogging exists in the entire column, and hydrodynamic dispersion increases sharply as aerobic and anaerobic microorganisms reproduce; (3) anaerobic microorganisms reproduce rapidly and produce more gas, and hydrodynamic dispersion decreases quickly; (4) aerobic and anaerobic microorganisms multiply continuously, and hydrodynamic dispersion, hydraulic conductivity, and porosity decrease steadily. Bioclogging then transforms into a steady stage.     

多孔介质渗透率的分形描述

针对土壤、岩石等多孔介质结构的复杂性,从其结构形成的物理机制和达西定律出发,利用分形几何理论,将土壤等作为在统计意义上具有分形特征的多孔介质来研究其水力参数与结构之间的关系,建立了饱和多孔介质渗透率与其分维数之间的定量化的函数式。试验应用扫描电镜法研究了多孔介质断面微结构并算出分维数。试验结果表明:利用该模型预测的多孔介质渗透率与实测值基本吻合,能够比较精确地预测多孔介质水力参数。     

Numerical solutions for flow in porous media

A numerical approach is proposed to model the flow in porous media using homogenization theory. The proposed concept involves the analyses of micro‐true flow at pore‐level and macro‐seepage flow at macro‐level. Macro‐seepage and microscopic characteristic flow equations are first derived from the Navier–Stokes equation at low Reynolds number through a two‐scale homogenization method. This homogenization method adopts an asymptotic expansion of velocity and pressure through the micro‐structures of porous media. A slightly compressible condition is introduced to express the characteristic flow through only characteristic velocity. This characteristic flow is then numerically solved using a penalty FEM scheme. Reduced integration technique is introduced for the volumetric term to avoid mesh locking. Finally, the numerical model is examined using two sets of permeability test data on clay and one set of permeability test data on sand. The numerical predictions agree well with the experimental data if constraint water film is considered for clay and two‐dimensional cross‐connection effect is included for sand. Copyright © 2003 John Wiley & Sons, Ltd.