Content uploaded by T. H. Illangasekare
Author content
All content in this area was uploaded by T. H. Illangasekare on Oct 13, 2014
Content may be subject to copyright.
Fingering of Dense Nonaqueous Phase Liquids in Porous Media: 2. Analysis and Classification
Water Resources Research
Abstract
Fingering of dense nonaqueous phase liquids (DNAPLs) as seen in three-dimensional experiments with saturated, homogeneous porous media was analyzed. A consistent geometrical quantification of finger configurations was obtained using concepts of fractal and multifractal scaling. Fractal patterns that determine the probabilistic distribution of the DNAPL were found to be representative for every experimental combination of sand and DNAPL. These patterns could be attributed to either capillary or viscous fingering regimes. With multifractal formalisms we were able to give a description of the underlying process kinetics. The generalized dimension D{sub q} relates results to diffusion-limited aggregation (DLA) or invasion percolation type models. The spectrum of singularities f({alpha}) is invariable for cross sections of an experiment and in turn can be used for a classification of the displacement system. The width of the f({alpha}) curve in the range of positive moments quantifies displacement instability. Phase transitions are indicated for the more stable displacement systems. 36 refs., 7 figs.
... Once released into the saturated subsurface, DNAPL migrates downwards through the pores as a result of flow instabilities induced by viscosity and density differences between liquid water and DNAPL. The displacing instabilities at the interface produce finger like appearance of the migrating DNAPL even in homogeneous saturated porous media (Held et al., 1995). This phenomenon is known as fingering. ...
... Many researchers have been involved in clarifying DNAPL fingering mechanism in saturated porous media by both laboratory imd field scale experiments. Most of the authors have pointed out the instability at the interface of the immiscible fluids as the primary reason for fingering (Kueper et al., 1988; Held et aI., 1995; Zhang Yuyong et aI., 2000; Oostrom et aI., 1999). Held et a1. ...
SYNOPSIS Knowledge of dense non-aqueous phase ,liquid (DNAPL) fingering phenomena in water-saturated porous media, which has not been investigated thoroughly, can be useful in gaining deeper insight into the contaminant transport and remediation. Laboratory experiments on fingering behaviors of trichloroethylene (TCE) through saturated porous media, randomly packed with uniform glass spheres in transparent glass box, were carried out. A basic mathematical model was developed and the experimental data on TCE fingering were interpreted based on it. The fingers grew almost linearly with time. The effective porosity of the media n e with three kind sizes of glass sphere (d =1, 2 and 3-mm) were between 4.0x10· 2 and 5.0x10· 2 irrespective of glass sphere size, while their invasion factor k r increased with pore size. Numerical values of k, varied from 5.0xlO-4 to 5.0x10· 2 in this study. TCE mobility and other fmgering characteristics were evaluated by using Zhang and Smith's mobile-immobile-zone (MIZ) model. Findings showed that core diameter t5 c of the fingers were almost the same while size of immobile zone t5 f increased with finger Reynolds number Re and relative intrinsic permeability K rd , which suggested that TCE with smaller mobility occupied wider pore space in the media. Values of Re in this study were in between 4.0 and 110.0. Thus, in this study we will deal with the difficulties of the fmgering phenomenon.
... Because fine-253 scale textural variability is not easily quantifiable in the field, these preferential pathways 254 can appear to be somewhat random in their distribution (see for example, Glass et al., 2000;255 Rathfelder et al., 2003). The propagation of fingers is more common in coarse textured media 256 and under conditions of low interfacial tension and high DNAPL density, since capillary forces 257 will tend to oppose the formation of extensive fingers (Held and Illangasekare, 1995). Given 258 their small lateral dimensions (typically less than a centimeter in width), fingers (and conse-259 quently, DNAPL migration pathways) are extremely difficult to locate in the field. ...
This chapter provides an overview of the challenges that impede successful remediation of chlorinated solvent source zones and recent advances in our ability to meet these challenges. The distribution (architecture) of DNAPL mass in these zones tends to be highly irregular, divided between ganglia and pools. Section 2 describes source zone architecture parameters or ‘metrics’ that may be used to describe DNAPL mass distribution characteristics that are associated with downgradient plume response, as well as efforts designed to predict and characterize DNAPL mass distribution. It is now generally understood that local groundwater concentrations can vary dramatically within a source zone region. Thus, increased attention is being focused on the quantification of mass flux as an alternative remedial endpoint. Section 3 presents an overview of recent research directed towards quantifying the relationship between DNAPL architecture and mass flux and developing tools for mass flux quantification and uncertainty analysis. To effectively design and implement in situ remediation technologies, it is essential that the overall extent, accessibility, composition, and spatial distribution of the DNAPL source zone is known. Detailed source zone characterization and real time monitoring can provide necessary data for targeted delivery of remedial agents, thereby minimizing costs and improving mass recovery. Section 4 explores the possible benefits of partial mass removal and the potential for using combined remedies to more effectively address DNAPL source zone management.
... Simple analytical relationships based on sediment and fluid properties successfully predicted the infiltration rate and final LNAPL lens thickness. In contrast, Held and Illangasekare [1995b] observed that 3-D DNAPL infiltration into homogeneous sediments was generally unstable and fingering was observed during flow; instability increased with increased pore size, with increased DNAPL density and decreased DNAPL viscosity, and finger development followed fractal patterns [Held and Illangasekare, 1995a]. Experimental and theoretical characterization of finger development and propagation has shown that fingers can develop as a result of pore-scale heterogeneity and fluid interactions, as well as macroscale heterogeneity [Darnault et al., 2001;Glass et al., 2000a;Gupta and Greenkorn, 1974;Huber et al., 2013;Ovdat and Berkowitz, 2006;Wang et al., 1998]. ...
Toxic organic contaminants may enter the subsurface as slightly soluble and volatile non-aqueous-phase-liquids (NAPLs) or as dissolved solutes resulting in contaminant plumes emanating from the source zone. A large body of research published in Water Resources Research has been devoted to characterizing and understanding processes controlling the transport and fate of these organic contaminants and the effectiveness of natural attenuation, bioremediation and other remedial technologies. These contributions include studies of NAPL flow, entrapment, and interphase mass transfer that have advanced from the analysis of simple systems with uniform properties and equilibrium contaminant phase partitioning to complex systems with pore- and macro-scale heterogeneity and rate-limited interphase mass transfer. Understanding of the fate of dissolved organic plumes has advanced from when biodegradation was thought to require oxygen, to recognition of the importance of anaerobic biodegradation, multiple redox zones, microbial enzyme kinetics, and mixing of organic contaminants and electron acceptors at plume fringes. Challenges remain in understanding the impacts of physical, chemical, biological and hydrogeological heterogeneity, pore-scale interactions, and mixing on the fate of organic contaminants. Further effort is needed to successfully incorporate these processes into field-scale predictions of transport and fate. Regulations have greatly reduced the frequency of new point source contamination problems; however, remediation at many legacy plumes remains challenging. A number of fields of current relevance are benefiting from research advances from point-source contaminant research. These include geologic carbon sequestration, nonpoint source contamination, aquifer storage and recovery, the fate of contaminants from oil and gas development, and enhanced bioremediation. This article is protected by copyright. All rights reserved.
... Density-driven instabilities can occur in a variety of subsurfaceflow processes, e.g. sea-water intrusion in coastal aquifers [15], geological storage of CO 2 [12,13,18], or in the presence of geothermal gradients [4,5]. As a consequence of the convective instability, rapidly moving fingers form, which can drastically reduce the travel time. ...
Simulation of density-driven instabilities requires flexible methods to deal with the different spatial and temporal scales involved. Downscaling approaches based on standard adaptive grid refinement aim at resolving the fine-scale details only in the region of interest, but they may become computationally expensive in presence of very corrugated unstable fronts because the problem to be solved approaches the size of the fully refined system. The Downscaling Multiscale Finite-Volume (DMsFV) method overcomes this issue by splitting the problems into a set of localized subproblems that interact only through a global problem. However, in presence of convective instabilities (e.g. density-driven fingers) the diffusion scale has to be resolved only at early times to capture the evolution of infinitesimal random perturbations, whereas at later times fingers have developed and merged, allowing the use of a coarser numerical description. Based on this observation, we present an adaptive algorithm which splits the simulation into three stages: an onset stage in which a set of localized problems is solved independently to capture the initial growth of the instabilities; a transition stage in which the DMsFV method is used to couple local and global scales; and a global stage in which only a fully coarsened description of the problem is employed. The dissolution-diffusion-convection problem (which is typically studied in the context of CO2 sequestration) is chosen as an example to evaluate the accuracy of the adaptive algorithm. For this problem, the use of a coarse grid that does not resolve the fine-scale details at earlier times leads to a dramatic underestimation of mass influx and penetration depth. On the contrary, the solutions obtained with the adaptive algorithm are in good agreement with the reference solution (obtained with a fully refined discretization) and are able to capture total mass influx and penetration depth with excellent accuracy. This demonstrates the need and the effectiveness of modeling local details during the instability onset to capture large-scale features of the concentration patterns at later times.
... Flow instabilities are common at displacement fronts between miscible or immiscible fluids. Gravity-driven instabilities in porous media, for instance, can be found during saltwater intrusion on coastal aquifers [15], water infiltration in dry soils [9,31], contamination of groundwater resources [12,13], or geological storage of carbon dioxide [6,7,33,20]. Depending on the density contrast, these instabilities, which are triggered by small-scale perturbations, can heavily affect large-scale flow and transport. ...
Accurate modeling of flow instabilities requires computational tools able to deal with several interacting scales, from the scale at which fingers are triggered up to the scale at which their effects need to be described. The Multiscale Finite Volume (MsFV) method offers a framework to couple fine- and coarse-scale features by solving a set of localized problems which are used both to define a coarse-scale problem and to reconstruct the fine-scale details of the flow. The MsFV method can be seen as an upscaling–downscaling technique, which is computationally more efficient than standard discretization schemes and more accurate than traditional upscaling techniques. We show that, although the method has proven accurate in modeling density-driven flow under stable conditions, the accuracy of the MsFV method deteriorates in case of unstable flow and an iterative scheme is required to control the localization error. To avoid large computational overhead due to the iterative scheme, we suggest several adaptive strategies both for flow and transport. In particular, the concentration gradient is used to identify a front region where instabilities are triggered and an accurate (iteratively improved) solution is required. Outside the front region the problem is upscaled and both flow and transport are solved only at the coarse scale. This adaptive strategy leads to very accurate solutions at roughly the same computational cost as the non-iterative MsFV method. In many circumstances, however, an accurate description of flow instabilities requires a refinement of the computational grid rather than a coarsening. For these problems, we propose a modified iterative MsFV, which can be used as downscaling method (DMsFV). Compared to other grid refinement techniques the DMsFV clearly separates the computational domain into refined and non-refined regions, which can be treated separately and matched later. This gives great flexibility to employ different physical descriptions in different regions, where different equations could be solved, offering an excellent framework to construct hybrid methods.
Numerous variations of Invasion-Percolation (IP) models can simulate multiphase flow in porous media across various scales (pore-scale IP to macroscopic IP); here, we are interested in gas flow in water-saturated porous media. This flow occurs either as continuous or discontinuous flow, depending on the flow rate and the porous medium’s nature. Literature suggests that IP models are well suited for the discontinuous gas flow regime; other flow regimes have not been explored. Our research compares four existing macroscopic IP models and ranks their performance in these “other” flow regimes. We test the models on a range of gas-injection in water-saturated sand experiments from transitional and continuous gas flow regimes. Using the light transmission technique, the experimental data is obtained as a time series of images in a 2-dimensional setup. To represent pore-scale heterogeneities, we ran each model version on several random realizations of the initial entry pressure field. We use a diffused version of the so-called Jaccard coefficient to rank the models against the experimental data. We average the Jaccard coefficient over all realizations per model version to evaluate each model and calibrate specific model parameters. Depending on the application domain, we observe that some macroscopic IP model versions are suitable in these previously unexplored flow regimes. Also, we identify that the initial entry pressure fields strongly affect the performance of these models. Our comparison method is not limited to gas-water systems in porous media but generalizes to any modelling situation accompanied by spatially and temporally highly resolved data.
This chapter presents a technology description of in situ chemical oxidation (ISCO) and discusses the key concepts associated with its use for remediation of chlorinated solvent dense nonaqueous phase liquid (DNAPL) source zones. A variety of oxidants are discussed including hydrogen peroxide, potassium permanganate, sodium persulfate and ozone. Current practices along with remedial design issues and approaches for application of ISCO to DNAPL source zones are described, including monitoring and optimization strategies. This chapter concludes with a discussion of emerging approaches and technologies, and a discussion of research needs and breakthrough areas.
Non-aqueous phase liquids (NAPLs) like petroleum hydrocarbons and chlorinated solvents have resulted in contamination of soils and ground water, which aroused widespread concern. It's quite important to delineate pollution area for remediation according to different soil types with pollutants properties in consideration. In this paper, a two-dimension visual sand box apparatus was constructed, with four typical NAPLs selected for infiltration experiments conducted in initially dry porous media. The main driving force was identified and fingering patterns were compared. The fractal dimension was used to give quantitative description. The present work indicates that the main driving force was capillary forces and the mechanism was the capillary fingering. The fingers varied from skeletal patterns to fleshy patterns and the infiltration area increased when the capillary number and the bond number decreased for NAPLs with the same level of viscosity. The high viscous force resulted in larger finger width and infiltration area. The same change between fluids happened in finer media. Fractal dimensions were positively correlated with the finger width and infiltration area, which is helpful in the pollution area characterization.
Understanding the mechanisms of how colloidal solution properties and drying processes result in dry colloidal structures is essential for industrial applications such as paint, ceramics, and electrodes. In this study, we develop a computational method to simulate the drying process of colloidal suspensions containing solid particles and polymers. The method consists of a solvent evaporation model, a fluid particle dynamics method, and a two-phase lattice Boltzmann method. We determine that a high-viscosity solvent, small surface tension, and a high evaporation rate of the solvent lead to a structure with dispersed particles and interconnected pores. When these conditions are not present, the particles agglomerate and the pores are disconnected.
The propagation of dense nonaqueous phase liquids (DNAPLs) in water-saturated, homogeneous porous media was investigated. The static distribution of DNAPL after gravity-driven displacement was studied using a number of three-dimensional spill experiments. Fingering intrinsic to the displacement systems was observed in all experiments. The effects of physical and chemical parameters on flow instability were examined for a range of sand grain sizes (fine, medium, and very coarse) and for different DNAPLs (trichloroethylene, trichloroethane, and dibutyl phthalate). Gravitational, viscous, and capillary forces were observed to have a varied influence on the flow behavior in these experiments. Our observations show that the development of finger patterns is sensitive to the porous media grain size, properties of the DNAPL, and spill conditions. By controlling experimental parameters, results are reproducible and yield insight into finger formation and preferential DNAPL flow in homogeneous aquifer materials. This paper discusses the experimental results qualitatively; a companion paper discusses their quantification with fractal concepts. 27 refs., 7 figs., 2 tabs.
The propagation of dense nonaqueous phase liquids (DNAPLs) in water-saturated, homogeneous porous media was investigated. The static distribution of DNAPL after gravity-driven displacement was studied using a number of three-dimensional spill experiments. Fingering intrinsic to the displacement systems was observed in all experiments. The effects of physical and chemical parameters on flow instability were examined for a range of sand grain sizes (fine, medium, and very coarse) and for different DNAPLs (trichloroethylene, trichloroethane, and dibutyl phthalate). Gravitational, viscous, and capillary forces were observed to have a varied influence on the flow behavior in these experiments. Our observations show that the development of finger patterns is sensitive to the porous media grain size, properties of the DNAPL, and spill conditions. By controlling experimental parameters, results are reproducible and yield insight into finger formation and preferential DNAPL flow in homogeneous aquifer materials. This paper discusses the experimental results qualitatively; a companion paper discusses their quantification with fractal concepts. 27 refs., 7 figs., 2 tabs.
What happens when one attempts to push water through a fluid of higher viscosity? Under appropriate experimental conditions, the water breaks through in the form of highly branched patterns called viscous fingers. Water was used to push a more viscous but miscible, non-newtonian fluid in a Hele-Shaw cell. The resulting viscous finger instability was found to be a fractal growth phenomenon. Reproducible values of the fractal dimension df were found and were interpreted using a modification of the diffusion limited aggregation model.
Published in Petroleum Transactions, AIME, Volume 216, 1959, pages 188–194.
Introduction
The purposes of this paper are to present theoretical and experimental evidence for occurrence of macroscopic instabilities in displacement of one viscous fluid by another immiscible with it through a uniform porous medium and to compare available experimental data with some predictions of a theory of instability developed by the first author.
The instabilities are referred to as macroscopic in the sense that spatially quasi-sinusoidal, growing fingers of the displacing liquid are formed, the width and peak-to-peak separation (wavelength) of which is large relative to a characteristic length of the particular permeable medium such as grain size.
Visual models of two kinds have been used to obtain observations: displacement of oil by water-glycerine solutions through the flow channel formed by closely spaced parallel plates and displacement of oil by water with and without initial interstitial water through unconsolidated glass powder packs, employing the technique of matching indices of refraction.
In all cases we have observed macroscopic instabilities or fingers under conditions predicted by the theory to be favorable for their occurrence.
The phenomenon discussed here is not the production of streamers due to gross inhomogeneities such as permeability stratification of the porous medium.It is our object to show, on the contrary, that a quantitative prediction of finger spacing is possible in a porous medium known to be macroscopically homogeneous and isotropic throughout.
The importance of the phenomenon in its influence on the configuration of oil and water with respect to oil production behavior was noted earlier by Engelberts and Klinkenberg who coined the term "viscous fingering".
Theory
Necessary and Sufficient Conditions for Instability and Initial Kinematics
There are several levels of increasing complexity in the theoretical description of instability of fluid displacements in permeable media. Of these, the simplest description, adapted to low permeability systems, is selected for presentation. More inclusive descriptions are reserved for separate publication.
We review briefly the formalism for studying multifractal scaling properties. The scaling structure is conveniently described by means of an f-α spectrum. For the onset of chaos via quasiperiodicity and period doubling we obtain universal spectra. These spectra are compared with spectra obtained from a forced Rayleigh-Benard experiment and very good agreement is found between theory and experiment. Finally, we show that the experimental spectra can be inverted and give information about the underlying dynamical process.
The displacement of a high viscosity fluid by a low viscosity fluid in a porous medium is a process of both scientific and practical importance. It has recently been shown by Chen and Wilkinson1 and by Måløy et al.2 that viscous fingering in a random porous medium at high capillary numbers, Ca > >10−4, generates structures with a fractal3 geometry. This fractal structure closely resembles that obtained from the diffusion limited aggregation (DLA) model of Witten and Sander4. Similar structures have also been obtained by fluid-fluid displacement in radial HeleShaw cells using non-Newtonian viscous fluids5. The relationship between fluid-fluid displacement in porous media and DLA was first discussed by Paterson6 and a more detailed analysis has been presented by Kadanoff7.
This paper presents a dimensionless number and its critical value for predicting the onset of instability during immiscible displacement in porous media. The critical dimensionless number obtained from a stability theory for a cylindrical system successfully predicted the onset of instability in laboratory floods. Therefore, this number can be used to classify the stability of two-phase incompressible displacements in homogeneous porous media.
Introduction
When a fluid displaces a more viscous fluid, the displacement front may become unstable, resulting in viscous fingering. This phenomenon raises both practical and theoretical concerns. Apart from further reducing the displacement efficiency of an already inefficient displacement arrangement, instability may invalidate the usual method of simulating immiscible displacement performance based on relative permeability and capillary pressure concepts. Also, it introduces an additional scaling requirement for using model tests to forecast prototype displacement results. Therefore, it would be most beneficial to predict the onset of instability, so as to avoid viscous fingering, or, where it is unavoidable, to be able to recognize it as a factor in the displacement.The onset of instability call be predicted by a stability analysis of the displacement. The objective of such an analysis is to determine the conditions under which small disturbances or perturbations of the displacement front will grow to become viscous fingers. Ideally, the analysis should give a universal dimensionless scaling group together with its critical value above which instability will occur. The stability classification then would entail no more than the calculation of one dimensionless number in a manner analogous to the calculation of a Reynolds number to distinguish between laminar and turbulent flow.Several stability studies of immiscible displacement have been reported in the literature. Collectively, they show that these variables are pertinent to the stability problem:mobility (or viscosity) ratio,displacement velocity, system geometry and dimensions,capillary and gravitational forces, andsystem permeability and wettability.
However, none of the previous studies have combined these variables into one dimensionless number that can be used to quantify the stability classification.The objective of this study was to obtain, by means of a stability analysis, a universal dimensionless scaling group and its critical value for predicting the onset of instability during immiscible displacement in porous media. This paper shows how the stability theory of Chuoke et al. was extended to achieve this objective and presents the results of laboratory floods that confirm the predicted onset of instability in cylindrical cores.
Theory
The pertinent dimensionless number for predicting the onset of instability was obtained by extending the stability theory of Chuoke et al. Their theory was based on a piston-like unperturbed displacement model in which the oil and water zones are separated by a planar interface. Details of the theory and our extension of it are presented in the following sections.
SPEJ
P. 249
Remarkable parallels in the behavior of diffusion-limited aggregation and two-fluid displacements in porous media exist; hence, the former can be used to simulate the latter. Both processes can be described by the application of Laplace's equation with similar boundary conditions. Displacements can be stabilized by reversing the flow direction and interfacial tension can be incorporated to broaden dendrites or fingers. Furthermore, diffusion-limited aggregation can be used to simulate flow in anisotropic or inhomogeneous porous media.
Slow, immiscible, viscoelastic liquid-liquid displacement in a permeable medium is considered. The necessary and sufficient criteria for stability are that the displacing fluid is denser and less mobile than the displaced one. The instability criteria and critical wavelength are found to be the same as those for ordinary viscous liquid-liquid displacements in permeable media.