Laboratory Study of Air Sparging: Air Flow Visualization

Laboratory flow visualization experiments, using glass beads as the porous medium, were conducted to study air sparging, an innovative technology for subsurface contaminant remediation. The purpose of these experiments was to observe how air flows through saturated porous media and to obtain a basic understanding of air plume formation and medium heterogeneity effects. The experiments indicate that air flow occurring in discrete, stable channels is the most probable flow behavior in medium to fine grained water saturated porous media and that medium heterogeneity plays an important role in the development of air channels. Several simulated scales of heterogeneities, from pore to field, have been studied. The results suggest that air channel formation is sensitive to the various scales of heterogeneities. Site-specific hydrogeologic settings have to be carefully reviewed before air sparging is applied to remediate sites contaminated by volatile organic compounds.     

Scaling of capillary,gravity and viscous forces affecting flow morphology in unsaturated porous media

Interplay between capillary, gravity and viscous forces in unsaturated porous media gives rise to a range of complex flow phenomena affecting morphology, stability and dynamics of wetting and drainage fronts. Similar average phase contents may result in significantly different fluid distribution and patterns affecting macroscopic transport properties of the unsaturated medium. The formulation of general force balance within simplified pore spaces yields scaling relationships for motion of liquid elements in which gravitational force in excess of capillary pinning force scales linearly with viscous force. Displacement fluid front morphology is described using dimensionless force ratios expressed as Bond and Capillary numbers. The concise representations of a wide range of flow regimes with scaling relations, and predictive capabilities of front morphology based on dimensionless numbers lend support to certain generalizations. Considering available experimental data, we are able to define conditions for onset of unstable and intermittent flows leading to enhanced liquid and gas entrapment. These results provide a basis for delineation of a tentative value of Bo ∼ 0.05 as an upper limit of applicability of the Richards equation (at pore to sample scales) and related continuum-based flow models.     

Stochastic analysis of immiscible displacement in porous media

The interface of two immiscible fluids flowing in porous media may behave in an unstable fashion. This instability is governed by the pore distribution, differential viscosity and interface tension between the two immiscible fluids. This study investigates the factors that control the interface instability at the wetting front. The development of the flow equation is based on the mass balance principle, with boundary conditions such as the velocity continuity and capillary pressure balance at the interface. By assuming that the two-phase fluids in porous media are saturated, a covariance function of the wetting front position is derived by stochastic theory. According to those results, the unstable interface between two immiscible fluids is governed by the fluid velocity and properties such as viscosity and density. The fluid properties that affect the interface instability are expressed as dimensionless parameters, mobility ratio, capillary number and Bond number. If the fluid flow is driven by gravitational force, whether the interface undergoes upward displacement or downward displacement, the variance of the unstable interface decreases with an increasing mobility ratio, increases with increasing capillary number, and decreases with increasing Bond number. For a circumstance in which fluid flow is horizontal, our results demonstrate that the capillary number does not influence the generation of the unstable interface.     

A fractal model for streaming potential coefficient in porous media

Streaming potential is the result of coupling between a fluid flow and an electric current in porous rocks. The modified Helmholtz–Smoluchowski equation derived for capillary tubes is mostly used to determine the streaming potential coefficient of porous media. However, to the best of our knowledge, the fractal geometry theory is not yet applied to analyse the streaming potential in porous media. In this article, a fractal model for the streaming potential coefficient in porous media is developed based on the fractal theory of porous media and on the streaming potential in a capillary. The proposed model is expressed in terms of the zeta potential at the solid?liquid interface, the minimum and maximum pore/capillary radii, the fractal dimension, and the porosity of porous media. The model is also examined by using another capillary size distribution available in published articles. The results obtained from the model using two different capillary size distributions are in good agreement with each other. The model predictions are then compared with experimental data in the literature and those based on the modified Helmholtz–Smoluchowski equation. It is shown that the predictions from the proposed fractal model are in good agreement with experimental data. In addition, the proposed model is able to reproduce the same result as the Helmholtz–Smoluchowski equation, particularly for high fluid conductivity or large grain diameters. Other factors influencing the streaming potential coefficient in porous media are also analysed.     

Slow gas expansion in saturated natural porous media by gas injection and partitioning with non-aqueous phase liquids

The partitioning of volatile non-aqueous phase liquid (NAPL) compounds to a discontinuous gas phase can result in the expansion of that gas phase, and the resulting gas flow can significantly affect the mass transfer from NAPL source zones. This recently reported gas flow generated by the spontaneous expansion of a discontinuous gas phase has not been extensively characterized in the literature. This study measured the expansion rate of a single gas cluster in a 1.1 mm sand above a pool of trans-1,2-dichloroethene (tDCE) in small-scale flow cell experiments. To characterize the gas flow, gas injection experiments in three sizes of sand were conducted at very slow injection rates typical of gas flow rates produced by gas expansion due to NAPL partitioning. Gas cluster spontaneous expansion rates above a tDCE pool were found to be 0.34 ± 0.02 and 0.29 ± 0.01 mL/day in duplicate experiments, which is sufficiently slow to result in discontinuous gas flow in porous media with a grain size diameter greater than 0.02 mm. Measured capillary pressures during gas injection showed patterns consistent with discontinuous gas flow, and identified multiple fragmentation events and expansion by coalescence with trapped clusters. The combination of pressure data and light transmission images were used to identify fragmentation and obtain direct measurements of the critical cluster length (i.e. the length at which withdrawal of the gas phase from a pore space occurs) in quasi-two-dimensional porous media for the first time. The measured critical cluster lengths were 1.4–3.6, 3.2–6.0 and 2.8–6.5 cm in 1.1, 0.7 and 0.5 mm sands, respectively. These values agreed well with estimates of the critical cluster length made using previously reported equations, and parameters derived from the medium’s capillary pressure-saturation relationship.     

Experimental studies on pathway patterns of secondary oil migration

The oil migration patterns in porous medium are discussed based on the results of diphasic expulsing experiments. In the experiments, dyed kerosene was used as expulsing phase to expulse water saturated in a glass cylinder filled with sorted glass beads. Two series of experiments were done: one with different initial oil column heights and the other with variable oil injection rates. Three secondary migration patterns, including stable displacement pattern, fingering pattern and stringing pattern may be recognized in each series of experiments. Two classic dimensionless parameters, the modified Bond number and the Capillary number, were used to construct a phase diagram that may characterize the patterns. A new method was proposed to calculate the Darcian velocity of moving kerosene in the cylinder when only buoyancy force acts. It is found that when Darcian velocity is used to get the two dimensionless parameters, the data from both series of experiments, as well as those obtained from literatures, may be reasonably drawn in a phase diagram to identify the three migration patterns.     

Clogging of saturated porous media by silt‐sized suspended solids under varying physical conditions during managed aquifer recharge

Managed aquifer recharge is an effective method for utilizing excess flood flows, but clogging of porous media is a limiting factor in the implementation of this water storage technique. In recent years, much research on the physical clogging of porous media during artificial recharge has been conducted. However, the understanding of clogging due to silt‐sized suspended solids (SS) is still inadequate, especially under varying physical conditions. Here, we subjected sand columns to controlled rates of flow and SS suspensions to investigate the influence of media size, SS size, SS concentration, and flow velocity on the clogging of porous media by silt‐sized SS. The results show that the diameter ratio of SS particles to sand grains is the dominant factor influencing the position of physical clogging. As pore velocity increased, the mobility of silt‐sized SS was enhanced and retention in the porous media decreased noticeably. The spatial retention profiles in the porous media were found to vary greatly at different flow velocities. The SS concentration of the infiltrating suspension also dramatically influenced the mobility and deposition of silt‐sized SS particles, such that high concentrations accelerated the clogging process. As the different physical factors changed, the breakthrough curves and retention profiles of silt‐sized SS particles changed obviously and the mechanisms of retention differed. On the whole, clogging position is mainly determined by particle size ratio, but clogging rate is dominated by a variety of factors including particle size ratio, SS concentration, and flow velocity.     

Impact of NAPL architecture on interphase mass transfer: A pore network study

Interphase mass transfer in porous media is commonly modeled using Sherwood number expressions that are developed in terms of fluid and porous medium properties averaged over some representative elementary volume (REV). In this work the influence of sub-grid scale properties on interphase mass transfer was investigated using a two-dimensional pore network model. The focus was on assessing the impact of (i) NAPL saturation, (ii) interfacial area (iii) NAPL spatial distribution at the pore scale, (iv) grain size heterogeneity, (v) REV or domain size and (vi) pore scale heterogeneity of the porous media on interphase mass transfer. Variability of both the mass transfer coefficient that explicitly accounts for the interfacial area and the mass transfer coefficient that lumps the interfacial area was examined. It was shown that pore scale NAPL distribution and its orientation relative to the flow direction have significant impact on flow bypassing and the interphase mass transfer coefficient. This results in a complex non-linear relationship between interfacial area and the REV-based interphase mass transfer rate. Hence, explicitly accounting for the interfacial area does not eliminate the uncertainty of the mass transfer coefficient. It was also shown that, even for explicitly defined flow patterns, changing the domain size over which the mass transfer process is defined influences the extent of NAPL bypassing and dilution and, consequently, the interphase mass transfer. It was also demonstrated that the spatial variability of pore scale parameters such as pore throat diameters may result in different rates of interphase mass transfer even for the same pore size distribution index.     

A stochastic model for air injection into saturated porous media

Air injection into porous media is investigated by laboratory experiments and numerical modelling. Typical applications of air injection into a granular bed are aerated bio-filters and air sparging of aquifers. The first stage of the dynamic process consists of air injection into a fixed or a quasi-fixed water-saturated granular bed. Later stages could include stages of movable beds as well, but are not further investigated here. A series of laboratory experiments were conducted in a two-dimensional box of the size 60 cm × 38 cm × 0.55 cm consisting of glass walls and using glass beads of diameter 0.4–0.6 mm as granular material. The development of the air flow pattern was optically observed and registered using a digital video camera. The resulting transient air flow pattern can be characterized as channelled flow in a fixed porous medium with dynamic tree-like evolution behaviour. Attempts are undertaken to model the air injection process. Multiphase pore-scale modelling is currently disregarded since it is restricted to very small scales. Invasion percolation models taking into account gravity effects are usually restricted to slow processes. On the other hand a continuum-type two-phase flow modelling approach is not able to simulate the observed air flow pattern. Instead a stochastic continuum-type approach is discussed here, which incorporates pore-scale features on a subscale, relevant for the immiscible processes involved. Consequently, the physical process can be modelled in a stochastic manner only, where the single experiment represents one of many possible realizations. However, the present procedure retains realistic water and air saturation patterns and therefore produces similar finger lengths and widths as observed in the experiments. Monte Carlo type modelling leads to ensemble mean water saturation and the related variance.     

Lithological and fluvial controls on the geomorphology of tropical montane stream channels in Puerto Rico

An extensive survey and topographic analysis of five watersheds draining the Luquillo Mountains in north‐eastern Puerto Rico was conducted to decouple the relative influences of lithologic and hydraulic forces in shaping the morphology of tropical montane stream channels. The Luquillo Mountains are a steep landscape composed of volcaniclastic and igneous rocks that exert a localized lithologic influence on the stream channels. However, the stream channels also experience strong hydraulic forcing due to high unit discharge in the humid rainforest environment. GIS‐based topographic analysis was used to examine channel profiles, and survey data were used to analyze downstream changes in channel geometry, grain sizes, stream power, and shear stresses. Results indicate that the longitudinal profiles are generally well graded but have concavities that reflect the influence of multiple rock types and colluvial‐alluvial transitions. Non‐fluvial processes, such as landslides, deliver coarse boulder‐sized sediment to the channels and may locally determine channel gradient and geometry. Median grain size is strongly related to drainage area and slope, and coarsens in the headwaters before fining in the downstream reaches; a pattern associated with a mid‐basin transition between colluvial and fluvial processes. Downstream hydraulic geometry relationships between discharge, width and velocity (although not depth) are well developed for all watersheds. Stream power displays a mid‐basin maximum in all basins, although the ratio of stream power to coarse grain size (indicative of hydraulic forcing) increases downstream. Excess dimensionless shear stress at bankfull flow wavers around the threshold for sediment mobility of the median grain size, and does not vary systematically with bankfull discharge; a common characteristic in self‐forming ‘threshold’ alluvial channels. The results suggest that although there is apparent bedrock and lithologic control on local reach‐scale channel morphology, strong fluvial forces acting over time have been sufficient to override boundary resistance and give rise to systematic basin‐scale patterns. Copyright © 2010 John Wiley and Sons, Ltd.     

A lattice Boltzmann study on the impact of the geometrical properties of porous media on the steady state relative permeabilities on two-phase immiscible flows

In the current paper, the effect of the geometrical characteristics of 2-D porous media on the relative permeability in immiscible two-phase flows is studied. The generation of the different artificial porous media is performed using a Boolean model based on a random distribution of overlapping circles/ellipses, the size and shape of which are chosen to satisfy the specific Minkowski functionals (i.e. volume fraction, solid line contour length, connectivity). The study aims to identify how each different Minkowski functional affects the relative permeability of each phase at various saturations of the non-wetting phase. A 2-D multi-relaxation time (MRT) lattice Boltzmann model (LBM) that can handle high density ratios is employed in the simulation. The relationship between the driving forces G and the relative permeabilities of the two phases for every artificial structure is quantified. It is found that for high non-wetting phase saturations (fully connected flow), a non-linear relationship exists between the non-wetting phase flow rate and the driving force, whilst this relationship becomes linear at higher magnitudes of the latter. The force magnitude required to approach the linear region is highly influenced by the pore size distribution and the connectivity of the solid phase. For lower non-wetting phase saturation values, its relative permeability in the linear regime decreases as the fraction of small pores in the structure increases and the non-wetting phase flow becomes disconnected. A strong influence of the solid phase connectivity is also observed.     

A study on the Wilkins and Forchheimer equations used in coarse granular media flow

Complexity of the pore geometry and the random nature of flow velocity make it difficult to predict and represent post laminar flow through porous media. Present study experimentally investigates the applicability of Forchheimer and Wilkins equations for post laminar flow where Darcy’s law is invalid due to predominant inertial effect. It is observed that both porosity and media size have significant influence over the coefficients of the Forchheimer coefficients. To incorporate the effect of porosity and media size, behaviour of Forchheimer coefficients are investigated with hydraulic radius as characteristic length. An inversely proportional variation trend is found for all the present and earlier reported data. A new empirical relation between Forchheimer coefficients and hydraulic radius is obtained which can be universally applicable for all media size and porosity. Coefficients of the Wilkins equation are found to be non-deviating for different hydraulic radius in the present study and in the reported literature validating its applicability in predicting the non laminar flow through porous media. Further the Wilkins equation is modified after incorporating the correction factors for better applicability on the field.     

A multiple-point statistics algorithm for 3D pore space reconstruction from 2D images

Fluid flow behavior in a porous medium is a function of the geometry and topology of its pore space. The construction of a three dimensional pore space model of a porous medium is therefore an important first step in characterizing the medium and predicting its flow properties. A stochastic technique for reconstruction of the 3D pore structure of unstructured random porous media from a 2D thin section training image is presented. The proposed technique relies on successive 2D multiple point statistics simulations coupled to a multi-scale conditioning data extraction procedure. The Single Normal Equation Simulation Algorithm (SNESIM), originally developed as a tool for reproduction of long-range, curvilinear features of geological structures, serves as the simulation engine. Various validating criteria such as marginal distributions of pore and grain, directional variograms, multiple-point connectivity curves, single phase effective permeability and two phase relative permeability calculations are used to analyze the results. The method is tested on a sample of Berea sandstone for which a 3D micro-CT scanning image is available. The results confirm that the equi-probable 3D realizations obtained preserve the typical patterns of the pore space that exist in thin sections, reproduce the long-range connectivities, capture the characteristics of anisotropy in both horizontal and vertical directions and have single and two phase flow characteristics consistent with those of the measured 3D micro-CT image.     

Visualization experiments of biodegradation in porous media and calculation of the biodegradation rate

Biodegradation in porous media is studied with carefully controlled and well-characterized experiments in model porous media constructed of etched glass. Porous media of this type allow visual observation of the phenomena that take place at pore scale. An aqueous solution of five organic pollutants (toluene, phenol, o-cresol, naphthalene and 1,2,3-trimethylbenzene) was used as a model NAPL (representing creosote). The bacteria used were Pseudomonas fluorescens, which are indigenous (even predominant) in many contaminated soils. The maximum aqueous concentrations of the specific organic substances, below which biodegradation becomes possible, were determined as a function of temperature from toxicity experiments. Visualization experiments were made under various flow velocities and organic loadings to study the morphology and thickness of the biofilm as a function of the pore size and the distance from the entrance, and the efficiency of biodegradation. The efficiency of biodegradation decreased as the aqueous concentration of NAPL at the inlet increased and/or as the flow velocity increased. The thickness of biofilm decreased as the distance from the inlet increased and/or the pore diameter decreased. A quasi-steady-state theoretical model of biodegradation was used to calculate the values of the mesoscopic biochemical rates and to predict the profile of NAPL concentration in the porous medium and the thickness of biofilm in pores. The agreement between experimental data and model predictions is quite satisfactory.     

A review of visualization techniques of biocolloid transport processes at the pore scale under saturated and unsaturated conditions

Field and column studies of biocolloid transport in porous media have yielded a large body of information, used to design treatment systems, protect water supplies and assess the risk of pathogen contamination. However, the inherent “black-box” approach of these larger scales has resulted in generalizations that sometimes prove inaccurate. Over the past 10–15 years, pore scale visualization techniques have improved substantially, allowing the study of biocolloid transport in saturated and unsaturated porous media at a level that provides a very clear understanding of the processes that govern biocolloid movement. For example, it is now understood that the reduction in pathways for biocolloids as a function of their size leads to earlier breakthrough. Interception of biocolloids by the porous media used to be considered independent of fluid flow velocity, but recent work indicates that there is a relationship between them. The existence of almost stagnant pore water regions within a porous medium can lead to storage of biocolloids, but this process is strongly colloid-size dependent, since larger biocolloids are focused along the central streamlines in the flowing fluid. Interfaces, such as the air–water interface, the soil–water interface and the soil–water–air interface, play a major role in attachment and detachment, with significant implications for risk assessment and system design. Important research questions related to the pore-scale factors that control attachment and detachment are key to furthering our understanding of the transport of biocolloids in porous media.     

裂缝-孔隙介质储层渗透率表征及其影响因素分析

含裂缝多孔介质渗透率预测是非常规油气资源勘探开发的一个紧迫问题.现有多孔介质岩石物理模型通常利用圆形孔管模拟宏观岩石孔隙空间,难以定量描述软孔隙/裂缝在压力作用下的闭合情况,缺乏裂缝/孔隙间流量交换的连通机制.本文提出含三维裂缝/软孔隙网络多孔介质模型,将储层岩石裂缝/软孔隙表示为椭圆截面微管,建立了周期性压力作用下微...     

Pore-scale imbibition experiments in dry and prewetted porous media

Two-phase imbibition behavior of immiscible fluids was studied in dry and prewetted porous media using a laser-induced fluorescence technique. Imbibition was first investigated in two-dimensional (2-D) systems under conditions comparable to those for a study of drainage [Ovdat H, Berkowitz B. Pore-scale study of drainage displacement under combined capillary and gravity effects in index-matched porous media. Water Resources Research 2006;42:W06411. doi:10.1029/2005WR004553] in the capillary-dominated regime. The effect of initial wetting saturation (IWS) was then explored in 2-D and 3-D porous media under the combined effect of gravity, capillary and viscous forces, within and outside the capillary-dominated regime. Parameters that describe maximum vertical advance, volumetric fraction, total surface area and specific surface area of the invading fluid were used to quantify the behavior. Comparison of 2-D drainage and imbibition patterns demonstrates significant qualitative differences under analogous viscosity ratio, buoyancy number, and capillary number values. However, quantitative analyses show strong pore-scale similarities between these patterns. Invasion structures in 3-D, prewetted (IWS ≈ 8% of the pore volume) porous media are ramified, with lateral branching and regions containing trapped residual fluid. These structures are qualitatively and quantitatively different from the compact, branchless structures that develop in dry (IWS = 0) porous media.     

FORCES ON PARTICLES AND THEIR EFFECTS ON VERTICAL SEDIMENT SORTING IN SOLID-LIQUID TWO-PHASE FLOWS

1 INNDUCTIONMes on prtcles are of significance to understand the motion of pwhcles in solid-liquid two-Phaseflows (Ni, et aI, l991). Early in l85l, Stokes (l85l) stUdied the simple harmonic linear motion of a singlesphere using a cylinder and a long flat plate. As a result, a simPle mathematical expression was given.Later on, Boussineaq (l885), Basset (1888), and Oseen (1927) stUdied the Iinear motion of a singIesphere that was accelotd in viscous fluid. It was fOund that the forces …     

Hierarchical simulator of biofilm growth and dynamics in granular porous materials

A new simulator is developed for the prediction of the rate and pattern of growth of biofilms in granular porous media. The biofilm is considered as a heterogeneous porous material that exhibits a hierarchy of length scales. An effective-medium model is used to calculate the local hydraulic permeability and diffusion coefficient in the biofilm, as functions of the local geometric and physicochemical properties. The Navier–Stokes equations and the Brinkman equation are solved numerically to determine the velocity and pressure fields within the pore space and the biofilm, respectively. Biofilm fragments become detached if they are exposed to shear stress higher than a critical value. The detached fragments re-enter into the fluid stream and move within the pore space until they exit from the system or become reattached to downstream grain or biofilm surfaces. A Lagrangian-type simulation is used to determine the trajectories of detached fragments. The spatiotemporal distributions of a carbon source, an electron acceptor and a cell-to-cell signaling molecule are determined from the numerical solution of the governing convection–diffusion–reaction equations. The simulator incorporates growth and apoptosis kinetics for the bacterial cells and production and lysis kinetics for the EPS. The specific growth rate of active bacterial cells depends on the local concentrations of nutrients, mechanical stresses, and a quorum sensing mechanism. Growth-induced deformation of the biofilms is implemented with a cellular automaton approach. In this work, the spatiotemporal evolution of biofilms in the pore space of a 2D granular medium is simulated under high flow rate and nutrient-rich conditions. Transient changes in the pore geometry caused by biofilm growth lead to the formation of preferential flowpaths within the granular porous medium. The decrease of permeability caused by clogging of the porous medium is calculated and is found to be in qualitative agreement with published experimental results.     

Quantifying gravel overlap and dislodgement forces on natural river bars: implications for particle entrainment

Equations for predicting particle entrainment typically assume that clast weight is the only factor resisting motion in the force balance on individual grains. In this work, increases in the force required to dislodge surface particles due to overlapping by surrounding clasts is quantified. Field data were collected at two subaerially‐exposed bars along the Colorado River in central Texas, USA, with median gravel diameters (D₅₀) of 37 and 64 mm. Clast size, shape, weight, the force required for vertical removal, and the fraction of clast area covered by surrounding grains were measured. Small hooks were glued to individual clasts without disrupting their positions and quasi‐static peak forces required to vertically dislodge each clast were measured using a force gauge. Clasts were also colored with dye before being dislodged, and image analysis was used to calculate the fraction of clast surface area covered by surrounding grains. The effect of overlap on the particle force balance is quantified by defining the ‘excess force ratio’ as the dislodgement force divided by the weight of the clast. Excess force ratio varies weakly but systematically with clast size: lifting larger clasts can require forces up to two times the clast's weight, while smaller clasts can require forces up to seven times their weight. The fraction of clast surface area covered by surrounding particles is also weakly correlated with excess force ratio. By assuming that critical shear stresses are proportional to the excess force ratio, the effect that overlap alone may have on particle entrainment is calculated. For a given size class, the most mobile grains should have critical shear stresses controlled only by their weight. However, clast overlap also causes broad distributions of critical stresses for partially‐exposed surface grains. The data quantify the significant fraction of bed area that should be less mobile than grain size alone would predict. Copyright © 2011 John Wiley & Sons, Ltd.