Mixing of miscible gas with oil in a reservoir decreases the effective strength of the gas, which can adversely affect miscibility and recovery efficiency. The mixing that occurs in a reservoir, however, is widely debated and often ignored in reservoir simulation, where very large grid blocks are used. Large grid blocks create artificially large mixing that can cause errors in predicted oil recovery. Reservoir mixing, or dispersion, is caused by diffusion of particles across streamlines of varying velocities. Mixing is enhanced by any mechanism that increases the area of contact between the gas and the oil, thereby allowing the effects of diffusion to be magnified. This is, in essence, the cause of scale-dependent dispersion. The contact area grows primarily because of variations in streamlines and their velocities around grains and through layers of various permeabilities (heterogeneity). Mixing can also be enhanced by crossflow, such as that caused by gravity and by the effects of other neighboring wells. This dissertation focuses on estimation of the level of effective local mixing at the field scale and its impact on oil recovery from miscible gas floods. Pore-level simulation was performed using the Navier-Stokes and convection-diffusion equations to examine the origin of scale dependent dispersion. We then estimated dispersivity at the macro scale as a function of key scaling groups in heterogeneous reservoirs. Lastly, we upscaled grid blocks to match the level of mixing at the pattern scale. Once the contact area ceases to grow with distance traveled, dispersion has reached its asymptotic limit. This generally occurs when the fluids are well mixed in transverse direction. We investigated a variety of pore-scale models to understand the nature of scale dependency. From the pore-scale study, we found that reservoir mixing or dispersion is caused by diffusion of particles across streamlines. Diffusion can be significantly enhanced if the surface area of contact between the reservoir and injected fluid are increased as fluids propagate through the reservoir. Echo and transmission dispersivities are scale dependent. They may or may not reach an asymptotic limit depending on the scale of heterogeneities encountered. The scale dependence results from an increase in the contact area between solute (gas) and resident fluid (oil) as heterogeneities are encountered, either at the pore or pattern-scale. The key scaling groups for first-contact miscible (FCM) flow are derived and their impact on mixing is analyzed. We examine only local mixing, not apparent mixing caused by variations in streamline path lengths (convective spreading). Local mixing is important because it affects the strength of the injected fluid, and can cause an otherwise multicontact miscible (MCM) flood to become immiscible. We then showed how to upscale miscible floods considering reservoir mixing. The sum of numerical dispersion and physical dispersion associated with the reservoir heterogeneities, geometry and fluid properties must be equal at both the fine- and large-scales. The maximum grid-block size allowed in both the x- and z-directions is determined from the scaling groups. Small grid-blocks must be used for reservoirs with uncorrelated permeabilities, while larger grid blocks can be used for more layered reservoirs. The predicted level of mixing for first-contact miscible floods can be extended with good accuracy to multicontact miscible (MCM) gas floods. / text

No description available.

The applicability and adequacy of three modeling approaches to describe and predict breakthough curves (BTCs) for non-reactive solutes in statistically homogeneous porous media were numerically and experimentally investigated. Modeling approaches were: the convection-dispersion equation (CDE) with scale-dependent dispersivity, mobile-immobile model (MIM), and the fractional convection-dispersion equation (FCDE). In order to test these modeling approaches, a prototype laboratory column system was designed for conducting miscible displacement experiments with a free-inlet boundary. Its performance and operating conditions were rigorously evaluated. When the CDE with scale-dependent dispersivity is solved numerically for generating a BTC at a given location, the scale-dependent dispersivity can be specified in several ways namely, local time-dependent dispersivity, average time-dependent dispersivity, apparent time-dependent dispersivity, apparent distance-dependent dispersivity, and local distance-dependent dispersivity. Theoretical analysis showed that, when dispersion was assumed to be a diffusion-like process, the scale-dependent dispersivity was locally time-dependent. In this case, definitions of the other dispersivities and relationships between them were directly or indirectly derived from local time-dependent dispersivity. Making choice between these dispersivities and relationships depended on the solute transport problem, solute transport conditions, level of accuracy of the calculated BTC, and computational efficiency The distribution of these scale-dependent dispersivities over scales could be described as either as a power-law function, hyperbolic function, log-power function, or as a new scale-dependent dispersivity function (termed as the LIC). The hyperbolic function and the LIC were two potentially applicable functions to adequately describe the scale dependent dispersivity distribution in statistically homogeneous porous media. All of the three modeling approaches described observed BTCs very well. The MIM was the only model that could explain the tailing phenomenon in the experimental BTCs. However, all of them could not accurately predict BTCs at other scales using parameters determined at one observed scale. For the MIM and the FCDE, the predictions might be acceptable only when the scale for prediction was very close to the observed scale. When the distribution of the dispersivity over a range of scales could be reasonably well-defined by observations, the CDE might be the best choice for predicting non-reactive solute transport in statistically homogeneous porous media. / Ph. D.

El proceso de dispersión de solutos en el seno de un medio poroso heterogéneo ha sido el objetivo de numerosas investigaciones en las últimas décadas debido tanto a las limitaciones de las ecuaciones matemáticas que lo describen como a la necesidad de describir y predecir el movimiento de contaminantes en acuíferos reales, con la complejidad derivada de los patrones espaciales de heterogeneidad reales y otras incertidumbres en el conocimiento del medio. Las técnicas de modelación actuales se centran generalmente en un único parámetro para explicar la desviación del comportamiento de un penacho de soluto frente a los resultados predichos por la ADE: la variabilidad de la conductividad hidráulica. En ningún caso se hace referencia o se tiene en cuenta la variabilidad espacial de la dispersividad. La dificultad para medir o estimar este parámetro y su enorme dependencia de la escala de la discretización numérica han limitado esta vía de investigación. Esta tesis presenta el primer intento de modelar la variabilidad local de la dispersividad basándose en un experimento de flujo y transporte de solutos en un tanque de experimentación de escala intermedia (Intermediate Scale Experiment, ISE). En esta investigación, se ha construido un medio poroso artificial inserto en un tanque de experimentación cuasi-2D, cuyos patrones de heterogeneidad estaban basados en datos de conductividad hidráulica procedente de una formación natural altamente heterogénea de características no gaussianas Controlando el potencial hidráulico a la entrada y la salida del tanque, se crearon condiciones de flujo estacionario en las que se llevaron a cabo varios ensayos de transporte de trazadores conservativos. Este tanque, construido en metacrilato, fue monitorizado con una red de transductores de presión de alta precisión y se tomaron fotografías digitales de la evolución del penacho de trazador coloreado. / Sanchez Fuster, I. (2011). Modelación de parámetros físicos de la ecuación de advección-dispersión utilizando un tanque de experimentación de escala intermedia [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/14635

Yes / Based on the Lagrangian approach, this study proposes a random displacement model (RDM) to predict the concentration of suspended sediment in vegetated steady open channel flow. Validation of the method was conducted by comparing the simulated results by using the RDM with available experimental measurements for uniform open-channel flows. The method is further validated with the classical Rouse formula. To simulate the important vertical dispersion caused by vegetation in the sediment-laden open channel flow, a new integrated sediment diffusion coefficient is introduced in this study, which is equal to a coefficient multiplying the turbulent diffusion coefficient. As such, the RDM approach for sandy flow with vegetation was established for predicting the suspended sediment concentration in low-sediment-concentration flow with both the emergent and submerged vegetation. The study shows that the value of for submerged vegetation flow is larger than that for emergent vegetation flow. The simulated result using the RDM is in good agreement with the available experimental data, indicating that the proposed sediment diffusion coefficient model can be accurately used to investigate the sediment concentration in vegetated steady open channel flow. / National Natural Science Foundation (No. 51439007, 11672213, and 11872285); Open Funding of State Key Laboratory of Water Resources and Hydropower Engineering Science (WRHES), Wuhan University (Project No: 2018HLG01)

Most soil particles loses cohesion and split up the soil mass into individual soil grains when they come in contact with water and get saturated. In dispersive soils the particles detach more spontaneously from each other and go into suspension even in quiet water. Thus the phenomenon of dispersion is common to most soils, the degree varying from soil to soil. Dispersive soils are abundantly found in various parts of the world such as Thailand, United States, Australia, Mexico, Brazil, South Africa and Vietnam. Several geotechnical failures such as piping due to internal erosion, erosion and gullying in relatively flat areas, collapse of sidewalls and topsoil removal have been reported worldwide due to the construction in dispersive soil. Failures as reported could be prevented if such soils are identified before-hand or if the quantification of dispersivity in the soil is done accurately. There are several methods of measuring dispersivity in soils which include several physical tests, chemical tests and some common laboratory tests. It is reported in literature that no method could be completely relied upon to identify dispersive soils with absolute confidence. In addition, when these methods were studied in detail, several flaws surfaced needing a better estimation of dispersivity. In order to develop a new method of estimation of dispersivity, the mechanism of dispersion in soils was studied in depth, which revealed that the existing concepts regarding dispersivity are incomplete in many aspects. An exhaustive philosophy of dispersion which addresses every detail is non-existing. To solve these problems, the concept of dispersivity was investigated in detail. It was found out that the observed dispersivity is a result of repulsion in the soil overcoming the attractive force. Thus a list of factors that could possibly affect the repulsion and attraction (and hence the dispersivity) in soils were found out. Even though literature focuses on exchangeable sodium as the principal reason for dispersivity, from fundamental theoretical considerations several other factors such as Cation exchange capacity (CEC), pH, structure of the soil, electrolyte concentration in the pore fluid, presence of organic matter, clay minerals involved in the soil and dissolved salts in the soil could possibly have an influence on dispersivity. Several studies have reported soils of high dispersivity to possess a high pH, high CEC, high amounts of sodium. The influence of these factors on dispersivity of other soils (or generally in any soil) is not well explored. Research on understanding their mechanism of action led to the conclusion that these parameters could be generalized for any soil. Through the analysis of these parameters, it was found that the fundamental parameter governing the dispersivity of soils is the number of charges on clay particles and that the repulsion in the soils is mainly contributed by the electrostatic repulsion. The attractive force in a soil/clay mass is primarily contributed by the van der Waal’s attraction and dispersion occurs when the electrostatic repulsion (resulting due to permanent and pH dependent charges) dominates over the van der Waal’s attraction. A practical estimation of charge with least effort could be possibly carried out through the measurement of zeta potential of soils. In order to verify whether the effect of all the factors is completely and sufficiently reflected in the zeta potential values, experiments were conducted on various soils. Three soils namely Suddha soil (a locally available dispersive soil), Black cotton soil and Red soil were selected for the study. These soils were chosen as the soil samples as they could display wide ranges of dispersivity values. In order to perform dispersivity tests, soil fraction finer than 75µ (75 micron meter sieve size) was fixed as the sample size as dispersivity pertaining to the finer fractions play a greater role than that of the coarser particles. All the three soil samples were treated with sodium hydroxide and urea solutions to alter the dispersivity so that the influence of all parameters could be studied. The dispersivity of the treated and untreated soils was found out through the various conventional tests and it was found that there exists a good correlation between the dispersivity and the zeta potential of soils. It was also observed that the increase in the dispersivity is higher when treated with salts of monovalent cations. Increase in the organic content also increased zeta potential, but not as significantly. One of the popularized theories on colloidal dispersions is the classical DLVO theory which has formulated the total interaction energy of colloidal particles by estimating the electrostatic repulsion and van der Waal’s attraction energy between two particles. The total interaction energy is then expressed as the difference between them. A similar approach as taken by the DLVO is adopted in this study. The total attractive energy existing in a soil mass is mathematically derived from the expression for van der Waal’s energy between two particles and the total repulsive energy from the zeta potential values. Two different approaches namely an infinitesimal particle approach and a finite particle approach is taken for finding the energy in a soil mass. In the infinitesimal particle approach, a clay particle is assumed to be infinitely small such that any soil particle of a finite radius could be conceived to be formed by a combination of infinite number of these infinitesimal particles. With this setting, the total energy in a soil mass is computed without really bothering about what exact particles constitute the mass. The increase in energy due to the increase in radius is then integrated to obtain the final expression. The dispersivity of the soil is then estimated under defined physical conditions of the soil. In the finite particle approach, each particle is considered to be of finite radius and to estimate the total energy, the total number of particle ombinations is then taken and the total energy is expressed as a sum of all the possible combinations. The dispersivity of a soil in both approaches is expressed as a release of energy when the repulsion rules over the attraction. In order to validate the derived propositions and expressions, experiments were conducted again on soils. The soils were treated with hydroxide salt of monovalent cations such as lithium, sodium and potassium. The dispersivity of the various treated and untreated soils was measured with the conventional methods and with the derived expressions of dispersivity through zeta potential. The similarity in the trend of the dispersivity values confirmed the validity of the derived expression. It was also concluded that the infinitesimal particle approach could be adopted when information about the physical properties are available and when they are not, the finite approach could be used. An accurate determination of zeta potential is critical for representation of dispersivity with zeta potential. Thus the procedure for measurement of zeta potential was standardized. The standardization was primarily focused on establishing the ideal conditions for zeta potential measurement. The role of Brownian motion, in electrophoretic mobility measurements were studied by employing the usage of zeta deviations. Untreated, potassium hydroxide treated, sodium hydroxide treated and lithium hydroxide treated samples of Suddha soil, Black Cotton soil and Red soil (finer than 75µ) were used for the study. Zeta potential measurements on unfiltered soil water suspensions, suspensions passing 2.5µ and suspensions passing 0.45µ were conducted along with recording their zeta deviations. It was observed that soil suspensions finer than 0.45µ show acceptable values of zeta deviations and thus could be used as a standard procedure for estimating zeta potentials. It was also concluded that the presence of Brownian motion makes the assessment of zeta potential through electrophoretic measurements easier and accurate. In an alternate perspective it as deduced that the amount of total monovalent ion concentration in the soil (dissolved and adsorbed) could adequately serves as an ideal parameter that could be used to quantify dispersion in soils. In order to verify the speculation, the variation of repulsive pressure with monovalent cation concentration was studied for the above mentioned treated and untreated soils. Within the monovalent cations, the role of ionic size in repulsion along with physical factors was also studied with the help of Atterberg limits, compaction characteristics, and dispersivity measurements. It could be concluded that even though there are several chemical factors such as CEC, pH, electrolyte concentration, type of clay minerals, dissolved salts etc. and physical factors such as plasticity, water holding capacity, density and structure which influence dispersion in soils, these factors affect either directly forces between the particles or the surface charge of clays which again affect the forces. The two phenomena can be combined through the hydration behaviour of the adsorbed cations on the clay surface in view of dispersivity. It is that force due to hydration which acts as the principal reason to separate the clay particles apart. As the radius of the inner hydration shell is higher for monovalent cations than those of higher valency ions, more force would be offered by the monovalent ions. Higher the charge and higher is the number of monovalent cations, higher will be the repulsion and thus the dispersivity. The repulsive force offered by the monovalent cations in soil was calculated through osmotic pressure differences and the dispersivity was expressed as the release of energy as earlier. In order to validate the proposal, the dispersivity of the samples as measured with the conventional methods was compared and studied with the derived expression. The similarity in the trend of the dispersity values confirmed the validity of the derived expressions. Thus, it can be seen that there are primarily two different methods of quantifying dispersivity of soils. When one method estimates dispersivity by calculating the electrostatic repulsion through zeta potential, the other method gives a dispersivity value based on the repulsive pressure offered by the monovalent cations in the soil. Two methods could be regarded as two different measurements of the electrical double layer. Any method could be used based on the property that could be easily quantified. The applicability of the new approaches – calculation of monovalent cations and zeta potential- for estimating the dispersivity in soils through a complete development of philosophy of dispersion and is presented, in this thesis, in nine chapters as follows: In Chapter 1 the background of the study and review of literature connected with the present study is presented. The mechanism of dispersion and the geotechnical problems associated with dispersion is elaborately presented in this section. As the dispersive soils cannot be identified through conventional tests, a description about the various tests designed to identify dispersive soils is presented. Earlier works relevant to the topic and the shortcomings of those studies are discussed. Finally, the objectives of the current research along with the scope of the work are explained in the concluding part of this chapter. Various factors that could have influence on the dispersivity of soils and their mechanism of action are presented in Chapter 2. The relationship of the factors with zeta potential is discussed. Theories dealing with dispersivity, conventional methods of measurement, role of geotechnical characteristics in assessing dispersivity are being presented. Chapter 3 deals with the various materials and methods used for the study. A locally available dispersive soil called Suddha soil along with Black Cotton soil and Red soil were chosen as the soils for the study of dispersion. The basic material properties and testing programs adopted for the study are presented in this chapter. The codal procedures followed to determine the physical, chemical, index and engineering properties are described in detail. The experimental investigations carried to bring out the role of zeta potential in dispersivity of soils are described in Chapter 4. Detailed analysis of the results showed estimation of zeta potential is possible and can sufficient quantify dispersivity of soils. The formulation of the equation for estimating dispersivity from zeta potential is described in Chapter 5. The estimation dispersivity based on attraction and repulsion energies in a soil mass is presented here. The adoption of the approach and methodologies used based on classical DLVO theory for the current work is explained in detail. The values of dispersivity obtained from the derived equation are compared with those obtained from the conventional tests. The validity of the expression is confirmed with the results of the experiments. Chapter 6 deals with the standardization of the measurement procedure of zeta potential. Role of Brownian motion in the accurate measurement of electrophoretic mobilities are brought out here. Chapter 7 brings out an alternate perspective of quantifying dispersivity through monovalent cations. The role of monovalent cations and the mechanism in which they contribute to the repulsive pressures (hence the dispersivity) are discussed. Experimental research design adopted has brought that the effect of monovalent and ionic size on repulsive pressures leading to dispersivity is described. The results of the experiments added with the inferences drawn are explained at the end. The estimation of repulsive pressures for measuring dispersivity from monovalent cations is discussed in Chapter 8. The dispersivity of a soil mass is derived from monovalent ion concentration and experiments were carried out for verification purposes. The experimental investigation procedure adopted followed by the results are presented in this chapter. It was observed that a good co-relation exists with the dispersivity obtained from the monovalent ion concentration and that obtained from conventional methods. Chapter 9 compares the dispersivity obtained through the various methods proposed in this thesis. The comparison is made in light of the classical electrical double layer theory. The major conclusions of the study are brought out at the end of this chapter.

Une des méthodes de récupération assistée du pétrole les plus utiliséesest l'injection de polymères. L'efficacité de cette méthode est attribuée principalement à laréduction de la mobilité de la phase aqueuse et à la viscoélasticité des polymères. Cetteefficacité dépend de plusieurs paramètres comme la perméabilité, la température, la salinité,l'hétérogénéité, la mouillabilité, le nombre capillaire, etc. De nombreuses connaissances ontété accumulées s’agissant du rôle des polymères dans la récupération du pétrole. Néanmoins,il subsiste encore des questions importantes:• Quel est le meilleur moment pour l’injection de polymère?• Quel rôle joue la mouillabilité dans la récupération ultime de pétrole?• Comment les effets viscoélastiques influencent-ils la récupération?• Quel est le rôle l’adsorption du polymère dans le processus de récupération?Cette thèse, expérimentale, a pour but de fournir des données concernant ledéplacement diphasique (en conditions de mouillabilité intermédiaire et de mouillabilité francheà l’eau) et d’investiguer l’impact réel de la rhéologie sur l’efficacité de déplacement de l’huile.Des injections de polymères sont réalisées à différents stades de précocité (c’est àdire, à différents moments après l’injection d’eau). Les résultats montrent un impact significatifde la précocité du balayage de polymère sur les taux de récupération finale et apparait commeun facteur déterminant à prendre en compte. D’autre part, on observe une récupération plusfaible pour une mouillabilité franche à l’eau que pour une mouillabilité intermédiaire etl’adsorption et la viscoélasticité de la solution de polymère ne sont pas déterminants dans letaux de récupération (dans nos conditions) alors que nos résultats indiquent un changementde mouillabilité durant l’injection de polymère.Des expériences complémentaires de dispersion diphasique ont ensuite mis enévidence un lien direct entre la dispersivité et le taux de récupération final. / Polymer flooding is one of the most developed chemical enhanced oil recoverymethod that has been used successfully since decades. In this chemical EOR method, thepolymer is adding to a waterflood to decrease its mobility. The resulting increase in viscosityas well as a decrease in aqueous phase permeability improve macroscopic oil sweepefficiency. At the pore scale, viscoelasticity is known to be also a key parameter that controlsthe microscopic sweep efficiency. However this sweep efficiency depends on several factorslike the permeability, temperature, salinity, wettability, capillary number, heterogeneity, etc.Therefore several studies are still necessary to have a better understanding of the behaviourof the polymer inside porous media and to optimize the process.• What is the best moment to inject polymer?• What is the role of wettability in final recovery?• How do viscoelastic effects influence recovery?• What is the role of adsorption of the polymer in the recovery process?In our interest to optimize and to understand polymer flooding process we have analysed thedependence of the sweep efficiency with the moment of the polymer injection duringwaterflooding and wettability (Water wet and intermediate wet). The polymer solution isinjected in the core at different maturity times (0PV, Breakthrough, 1PV, 2PV, 3PV, 4PV and6PV).The main results can be summarized in three points .The results show oil recoveryfinal for water wet corefloods is lower than intermediate wet corefloods. On the other hand, theproduction of oil with the injection of polymer is higher than the injection of water due to afavorable mobility ratio. Finally, the final recovery rates are lower when the polymer injectionis late. These results suggest that the history of sweeping can lead to different distributions ofphases (oil/brine) at the end of the waterflood. The sweep efficiency is related to the ability ofthe polymer to disperse throughout the accessible portal space. We have analysed this aspectfrom the point of view of the diphasic dispersion by showing that the dispersivity of the phasesis different at each time of the water injection. The complementary diphasic dispersionexperiments showed a direct link between dispersivity and the final oil recovery.

Made available in DSpace on 2015-03-26T13:23:35Z (GMT). No. of bitstreams: 1 texto completo.pdf: 1110634 bytes, checksum: 2fca1d4f36b7153de287bd841f14152d (MD5) Previous issue date: 2011-02-10 / Conselho Nacional de Desenvolvimento Científico e Tecnológico / The effectiveness of the mathematical models developed to describe the solute transport in the soil depends on the reliability of the values of the transport parameters. Although the determination of these parameters use the same transport equation, some experimental conditions such as the column length and the pore water velocity does not have standards, making questionable the results and the comparison of different researches. Thus, the aim of this study was to evaluate the influence of flow velocity and the length of soil column to determine the coefficient of dispersion-diffusion (D), dispersivity (λ) and the retardation factor (R) of the potassium ion (K+) on an Oxisol (clay soil) and on a Dystric Quartzarenic Neosol (sandy soil). The experiment was conducted in a laboratory using, for each soil, columns of lengths (L) equals to 10, 20, 30, 40 and 50 cm, with an internal diameter of 47 mm and pore water velocities equal to (v) 61.9, 69.12, 74.88 and 80.86 cm h-1 for the clay soil and 37.16, 40.57, 48.07 and 44.0 cm h-1 for the sandy soil. The columns repacked and saturated with a solution of CaCl2, 0.005 mol L-1 were connected to a Mariotte bottle, containing the same solution of CaCl2, until a steady flow is achieved. Later, it was applied the head that would provide the desired pore water velocity according to the hydraulic conductivity and total porosity of the column, and then the solution was replaced by a KCl solution containing 130 mg L-1 of K+. The effluent of the solution of K+ was collected until seven pore volumes for clay soil and five pore volumes for sandy soil were achieved. These pore volumes were divided into 18 samples of about 0.28 and 0.39 pore volumes for sandy and clay soil, respectively. The R and D transport parameters were obtained using the Disp computer program and the λ was obtained by the equation D = Do + λv, being Do equal to 0.0713 cm2 h-1 for the KCl. For both soils, D increased linearly with L and v and the λ linearly increased with L. The R, for the clay soil, linearly decreased with L and increased with v. For the sandy soil, the R had a linear decreased in terms of L. It can be concluded that the solute transport parameters were influenced by the length of soil column and the pore water velocity. / A eficácia dos modelos matemáticos desenvolvidos para descrever o transporte de solutos no solo depende do grau de confiabilidade dos valores dos parâmetros de transporte. Apesar dos trabalhos de determinação destes parâmetros utilizarem a mesma equação de transporte, algumas condições experimentais como o comprimento da coluna e a velocidade de deslocamento da solução aplicada não têm padronização, tornando questionáveis os resultados obtidos e a comparação destes com outros trabalhos. Com isso, este estudo objetivou avaliar a influência da velocidade de escoamento e do comprimento da coluna de solo na determinação do coeficiente de dispersão-difusão (D), da dispersividade (λ) e do fator de retardamento (R) do íon potássio (K+) em um Latossolo Vermelho distrófico (LVd) e num Neossolo Quartizarênico órtico (RQo). O experimento foi realizado em laboratório, utilizando, para cada solo, colunas de lixiviação de comprimento (L) iguais a 10, 20, 30, 40 e 50 cm, com 4,7 cm de diâmetros internos e velocidades de escoamento da solução (v) de 61,9; 69,12, 74,88 e 80,86 cm h-1 para o LVd e de 37,16; 40,57, 44,0 e 48,07 cm h-1 para o RQo. As colunas, preenchidas com o solo desestruturado e saturado com solução de CaCl2, 0,005 mol L-1, foram conectadas a permeâmetros de carga constante contendo a mesma solução de CaCl2 até se obter escoamento permanente. Posteriormente, aplicava-se a carga que proporcionaria a velocidade desejada de acordo com a condutividade hidráulica da coluna e a porosidade total e, em seguida substituía-se a solução por uma de KCl contendo 130 mg L-1 de K+. O efluente da solução de K+ foi coletado até atingir sete volumes de poros para o LVd e cinco volumes de poros para o RQo, sendo que esses volumes foram divididos em 18 coletas de aproximadamente 0,28 e 0,39 volumes de poros para o RQo e o LVd, respectivamente. Os parâmetros de transporte R e D foram obtidos utilizando-se o programa computacional Disp e a λ foi obtida pela equação D = Do + λv, sendo Do igual a 0,0713 cm2 h-1 para o KCl . Para os dois solos, D apresentou ajuste de regressão linear múltipla positiva em função de L e de v com R² = 0,79 para o LVd e R² = 0,85 para o RQo, o parâmetro λ ajustou-se a regressão linear simples positiva em função de L com R² = 0,92 e R² = 0,93 para o LVd e o RQo, respectivamente. O R, para o LVd, apresentou ajuste de regressão linear simples negativa em função de L (R² = 0,87) e positiva em função de v (R² = 0,68). Para o RQo, o R apresentou ajuste de regressão linear simples negativa em função de L (R² = 0,79). Pode-se concluir que os parâmetros de transporte de solutos foram influenciados pelo comprimento da coluna de solo e pela velocidade de escoamento da solução deslocadora.

Analysis of flow and solute transport problem in porous media are affected by uncertainty inbuilt both in boundary conditions and spatial variability in system parameters. The experimental investigation reveals that the parameters may vary in various scales by several orders. These affect the solute plume characteristics in field-scale problem and cause uncertainty in the prediction of concentration. The main focus of the present thesis is to analyze the probabilistic behavior of solute concentration in three dimensional(3-D) heterogeneous porous media. The framework for the probabilistic analysis has been developed using perturbation approach for both spectral based analytical and finite element based numerical method. The results of the probabilistic analysis are presented either in terms of solute plume characteristics or prediction uncertainty of the concentration. After providing a brief introduction on the role of stochastic analysis in subsurface hydrology in chapter 1, a detailed review of the literature is presented to establish the existing state-of-art in the research on the probabilistic analysis of flow and transport in simple and complex heterogeneous porous media in chapter 2. The literature review is mainly focused on the methods of solution of the stochastic differential equation. Perturbation based spectral method is often used for probabilistic analysis of flow and solute transport problem. Using this analytical method a nonlocal equation is solved to derive the expression of the spatial plume moments. The spatial plume moments represent the solute movement, spreading in an average sense. In chapter 3 of the present thesis, local dispersivity if also assumed to be random space function along with hydraulic conductivity. For various correlation coefficients of the random parameters, the results in terms of the field scale effective dispersivity are presented to demonstrate the effect of local dispersivity variation in space. The randomness of local dispersivity is found to reduce the effective fields scale dispersivity. The transverse effective macrodispersivity is affected more than the longitudinal effective macrodispersivity due to random spatial variation of local dispersivity. The reduction in effective field scale longitudinal dispersivity is more for positive correlation coefficient. The applicability of the analytical method, which is discussed in earlier chapter, is limited to the simple boundary conditions. The solution by spectral method in terms of statistical moments of concentration as a function of space and time, require higher dimensional integration. Perturbation based stochastic finite element method(SFEM) is an alternative method for performing probabilistic analysis of concentration. The use of this numerical method for performing probabilistic analysis of concentration. The use of this numerical method is non common in the literature of stochastic subsurface hydrology. The perturbation based SFEM which uses FEM for spatial discretization of the steady state flow and Laplace transform for the solute transport equation, is developed in chapter 4. The SFEM is formulated using Taylor series of the dependent variable upto second-order term. This results in second-order accurate mean and first-order accurate standard deviation of concentration. In this study the governing medium properties viz. hydraulic Conductivity, dispersivity, molecular diffusion, porosity, sorption coefficient and decay coefficient are considered to vary randomly in space. The accuracy of results and computational efficiency of the SFEM are compared with Monte Carle Simulation method(MCSM) for both I-D and 3-D problems. The comparison of results obtained hby SFEM and MCSM indicates that SFEM is capable in providing reasonably accurate mean and standard deviation of concentration. The Laplace transform based SFEM is simpler and advantageous since it does not require any stability criteria for choosing the time step. However it is not applicable for nonlinear transport problems as well as unsteady flow conditions. In this situation, finite difference method is adopted for the time discretization. The first part of the Chapter 5, deals with the formulation of time domain SFEM for the linear solute transport problem. Later the SFEM is extended for a problem which involve uncertainty of both system parameters and boundary/source conditions. For the flow problem, the randomness in the boundary condition is attributed by the random spatial variation of recharge at the top of the domain. The random recharge is modeled using mean, standard deviation and 2-D spatial correlation function. It is observed that even for the deterministic recharge case, the behavior of prediction uncertainty of concentration in the space is affected significantly due to the variation of flow field. When the effect of randomness of recharge condition is included, the standard deviation of concentration increases further. For solute transport, the concentration input at the source is modeled as a time varying random process. Two types of random source at the source is modeled as a time varying random process. Two types of random source condition are considered, firstly the amount of solute mass released at uniform time interval is random and secondly the source is treated as a Poission process. For the case of multiple random mass releases, the stochastic response function due to stochastic system is obtained by using SFEM. Comparing the results for the two type of random sources, it sis found that the prediction uncertainty is more when it is modeled as a Poisson process. The probabilistic analysis of nonlinear solute transport problem using MCSM is often requires large computational cost. The formulation of the alternative efficient method, SFEM, for nonlinear solute transport problem is presented in chapter 6. A general Langmuir-Freundlich isotherm is considered to model the equilibrium mass transfer between aqueous and sorbed phase. In the SFEM formulation, which uses the Taylor Series expansion, the zeroth-order derivatives of concentration are obtained by solving nonlinear algebraic equation. The higher order derivatives are obtained by solving linear equation. During transport, the nonlinear sorbing solutes is characterized by sharp solute fronts with a traveling wave behavior. Due to this the prediction uncertainty is significantly higher. The comparison of accuracy and computational efficiency of SFEM with MCSM for I-D and 3-D problems, reveals that the performance of SFEM for nonlinear problem is good and similar to the linear problem. In Chapter 7, the nonlinear SFEM is extended for probabilistic analysis of biodegrading solute, which is modeled by a set of PDEs coupled with nonlinear Monod type source/sink terms. In this study the biodegradation problem involves a single solute by a single class of microorganisms coupled with dynamic microbial growth is attempted using this methods. The temporal behavior of mean and standard deviation of substrate concentration are not monotonic, they show peaks before reaching lower steady state value. A comparison between the SFEM and MCSM for the mean and standard deviation of concentration is made for various stochastic cases of the I-D problem. In most of the cases the results compare reasonably well. The analysis of probabilistic behavior of substrate concentration for different correlation coefficient between the physical parameters(hydraulic conductivity, porosity, dispersivity and diffusion coefficient) and the biological parameters(maximum substrate utilization rate and the coefficient of cell decay) is performed. It is observed that the positive correlation between the two sets of parameters results in a lower mean and significantly higher standard deviation of substrate concentration. In the previous chapters, the stochastic analysis pertaining to the prediction uncertainty of concentration has been presented for simple problem where the system parameters are modeled as statistically homogeneous random. The experimental investigations in a small watershed, point towards a complex in geological substratum. It has been observed through the 2-D electrical resistivity imaging that the interface between the layers of high conductive weathered zone and low conductive clay is very irregular and complex in nature. In chapter 8 a theoretical model based on stochastic approach is developed to stimulate the complex geological structure of the weathered zone, using the 2-D electrical image. The statistical parameters of hydraulic conductivity field are estimated using the data obtained from the Magnetic Resonance Sounding(MRS) method. Due to the large complexity in the distribution of weathered zone, the stochastic analysis of seepage flux has been carried out by using MCSM. A batter characterization of the domain based on sufficient experimental data and suitable model of the random conductivity field may help to use the efficient SFEM. The flow domain is modeled as (i) an unstructured random field consisting of a single material with spatial heterogeneity, and (ii) a structured random field using 2-D electrical imaging which is composed of two layers of different heterogeneous random hydraulic properties. The simulations show that the prediction uncertainty of seepage flux is comparatively less when structured modeling framework is used rather than the unstructured modeling. At the end, in chapter 9 the important conclusions drawn from various chapters are summarized.

The aim of the present investigation is to improve the geotechnical properties of dispersive soil by reducing their dispersivity after elucidating the important mechanisms controlling the dispersivity of the soils. Dispersive soils have unique properties, which under certain conditions deflocculate and are rapidly eroded and carried away by water flow. These soils are found extensively in the United States, Australia, Greece, India, Latin America, South Africa and Thailand. The mechanism of dispersivity of soils is a subject matter of great interest for geotechnical engineers. In the earlier days clays were considered to be non erosive and highly resistant to water erosion. However, recently it was found that highly erosive clay soils do exist in nature. Apart from clayey soil, dispersivity is also observed in silty soils. The tendency of the clays to disperse or deflocculate depends upon the mineralogy and soil chemistry and also on the dissolved salts in the pore water and the eroding water. Such natural dispersive soils are problematic for geotechnical engineers. They are clayey soils which are highly susceptible to erosion in nature and contain a high percentage of exchangeable sodium ions, (Na+). It is considered that the soil dispersivity is mainly due to the presence of exchangeable sodium present in the structure. When dispersive clay soil is immersed in water, the clay fraction behaves like single-grained particles; that is, the clay particles have a minimum of electrochemical attraction and fail to closely adhere to, or bond with, other soil particles. This implies that the attractive forces are less than the repulsive forces thus leading to deflocculation (in saturated condition).This weakens the aggregates in the soil causing structural collapse. Such erosion may start in a drying crack, settlement crack, hydraulic fracture crack, or other channel of high permeability in a soil mass. Total failure of slopes in natural deposits is initiated by dispersion of clay particles along cracks, fissures and root holes, accelerated by seepage water. For dispersive clay soils to erode, a concentrated leakage channel such as a crack (even a very small crack) must exist through an earth embankment. Erosion of the walls of the channel then occurs along the entire length at the same time. Many slope and earth dam failures have occurred due to the presence of dispersive soils. Unlike erosion in cohesionless soils, erosion in dispersive clay is not a result of seepage through the pores of clay mass. However, the role of type of clay and its Cation exchange capacity in the dispersion of soil is not well understood. Data on the presence, properties, and tests for identification of dispersive clays is scarce. Hence, an attempt is made, in this thesis, to develop reliable methods to identify these soils and understand the extent of their dispersivity as well as to develop methods to control their dispersivity. The present study deals with the characterization of a local dispersive soil collected from southern part of Karnataka State. This study has focused on comprehensive tests to assess the dispersivity of the soils by different methods and to methods to improve geotechnical properties by reducing the dispersivity of the soil. An attempt is made to reduce the dispersivity of soil by using calcium based stabilizers such as lime, cement and fly ash. The mechanism of improvement in reducing the dispersivity of the soil with calcium based stabilizers has been studied. One of the important mechanism by which the dispersivity of the soil is reduced is by inducing cementation of soil particles. The differences in effectiveness of different additives are due to their differences in abilities to produce cementitious compounds. Although all the additives increased the strength of the soil and reduced the dispersivity of the soil, cement was found to significantly reduce the dispersivity of the soil, compared to the other two additives lime and fly ash. Cement is more effective as sufficient cementitious compounds are produced on hydration without depending on their formation. A detailed review of literature on all aspects connected with the present study is given in Chapter 2. A comprehensive description of dispersive soils present worldwide has been brought out in this section. Based on this survey, the scope of the present investigation has been elaborated at the end of the chapter. To understand the reasons for dispersivity of the soil and to estimate its degree of dispersivity, it is essential to assess standard methods to characterize the soil. Chapter 3 presents a summary of material properties and testing programs. The results of geotechnical characterization of the soil, the index properties of the soilspecific gravity, sieve analysis, Atterberg’s limits are discussed in Chapter 4. The physico chemical characteristics play an important role in determining the amount of dispersivity of the soil. Dispersive soils have two main characteristics which define its dispersivity chemically. These are Sodium Adsorption Ratio (S.A.R) and Exchangeable Sodium Percentage (E.S.P). The two characteristics are determined from the Cation exchange capacity of the soil. Exchangeable Sodium Percentage is defined as the concentration of sodium ions present in the soil with respect to the Cat ion exchange capacity of the soil. And Sodium Adsorption Ratio is used to quantify the free salts present in the pore water. Since Atterberg’s limits and grain size analysis do not help in identifying dispersive soils or in quantifying its dispersivity, two other tests- Emerson Crumb test and double hydrometer test were carried out on the soil. Emerson crumb test is a simple way for identification of dispersive soils. In this test, a crumb of soil measuring about 1mm diameter is immersed in a beaker containing distilled water and the subsequent reaction is observed for 5 minutes. It is solely based on direct qualitative observations. Depending on the degree of turbidity of the cloud formed in the beaker, the soil is classified in one of the four levels of dispersion in accordance with ASTM-D6572. Since this test is mainly a qualitative test and does not help in quantifying the dispersivity, it cannot be depended upon completely in identifying a dispersive soil. Another test double hydrometer test, which helps in quantifying the dispersivity of the soil, was also conducted on the soil. This test involves in conducting the particle size distribution using the standard hydrometer test in which the soil specimen was dispersed in distilled water with a chemical dispersant. A parallel hydrometer test was conducted on another soil specimen, but without a chemical dispersant. The dispersing agent used for the experiment was sodium hexametaphosphate. The percent dispersion is the ratio of the dry mass of particles smaller than 0.005 mm diameter of the test without dispersing agent to the test with dispersing agent expressed as a percentage. The double hydrometer test was carried out according to Double Hydrometer Test (ASTM D4221). Apart from the conventional tests, attempts are made to consider shrinkage limit test and unconfined compression test to determine the dispersivity of the soil. For this purpose, the shrinkage limit of the soil was determined with and without dispersing agent. The initial shrinkage limit of the untreated soil reduced on treating it with dispersing agent, thus indicating that the soil had further dispersed on addition of dispersing agent. In order to carry out the unconfined compression strength, the maximum dry density and optimum moisture content was determined through the compaction test. The soil was then treated with dispersing agent and compacted at the optimum moisture content. The soil exhibited high degree of dispersion through the strength test. Hence it is necessary to stabilize the soil with additives. Detailed experimental program has been drawn to find methods to improve the geotechnical properties and to reduce the dispersivity of the soil. Chapter 5 presents the investigations carried out on the dispersive soil with lime. The importance of lime stabilization and the mechanism of lime stabilization have been discussed initially. Commercially obtained hydrated lime was used in the present study. The soil was treated with three different percentages of lime 3, 5 and 8. The curing period was varied from one day to twenty eight days. The effect of addition of lime on various properties of the soil such as pH, Atterberg’s limits, compaction test and unconfined compression test is elaborated in chapter 5. The pH of the soil was maximum on addition of 3% lime. On further addition, the pH decreased and remained constant. The liquid limit of the soil increased on adding 3% lime and decreased with further lime content. The compaction test conducted on the soil showed an increase in maximum dry density of the soil and reduction in optimum moisture content with 3% lime content. On further increase in the lime content, the soil showed a decrease in the maximum dry density and increase in optimum moisture content. The unconfined compressive strength of the soil also increased on increasing lime content upto 5%. The variation in strength of the soil with respect to curing period was also compared. Optimum lime content arrived at based on the above conducted tests was 3%. The effect of lime in reducing the dispersivity of the soil through shrinkage limit test and unconfined compression test is also presented in this chapter. Details of the efforts made on the soil with fly ash are presented in Chapter 6.The fly ash used for stabilization of Suddha soil was of Class F type. This type of fly ash contains low reactive silica and lime. The effect of varying fly ash content on the properties of Suddha soil by varying the percentage of fly ash from 3 to 10 percentages is discussed in this chapter. The tests conducted on fly ash treated Suddha soil were pH test, compaction test, Atterberg’s limits and unconfined compression test with varying curing period. The fly ash treated Suddha soil was cured from one day to twenty eight days for the unconfined compressive strength analysis. The pH of the soil system increased with increasing percentage of fly ash. The increase in liquid limit was marginal on addition of fly ash. The maximum dry density of fly ash treated Suddha soil decreased continuously and the optimum moisture content of the treated soil increased with increasing fly ash content. The unconfined compressive strength of Suddha soil increased with increase in fly ash content upto 8% and then decreased for fly ash content of 10%. For all the percentages of fly ash added, the strength of the soil increased with increase in the curing period. The effect of fly ash in reducing the dispersivity of the soil was carried out using shrinkage limit and unconfined compression test. It was seen that on increasing the fly ash content, the soil treated with dispersing agent showed an increase in the shrinkage limit. Also, the same trend was observed for the unconfined compression strength to determine dispersivity. Optimum fly ash was determined as 8% with the help of all the tests conducted on the soil. Since the improvement in the properties of the soil with lime and fly ash was not very high, Cement was also considered as another additive used for stabilization of Suddha soil. It is known that soil with lesser amount of clay content will respond well with cement. The effect of cement addition on various properties of Suddha soil has been brought out in Chapter 7. It was found that addition of cement had positive effects on all the properties of Suddha soil. The pH of the soil increased for all the percentages of cement addition. The liquid limit of the soil increased on increasing the cement content. The shrinkage limit also showed a similar trend. The optimum moisture content of the soil decreased on increasing the cement content for Suddha soil and the maximum dry density increased for cement treated Suddha soil. The soil showed the maximum dry density at 8% cement content. The unconfined compression strength conducted on cement treated Suddha soil increased significantly for higher cement contents and also with curing period. Suddha soil when treated with 8% cement content exhibited maximum strength in comparison to other percentages. Also, the effect of cement in reducing the dispersivity of the soil was carried out using shrinkage limit and unconfined compression test. The shrinkage limit of the soil increased for all percentages of cement content, even in the presence of dispersing agent. Through the unconfined compression strength for dispersivity, it could be seen that 8% cement treated Suddha soil had the least dispersion. Optimum cement content was derived as 8% with the help of the tests conducted on the soil. A comparison of effect of all the additives on the strength of the soil as well as effect of the additives in reducing the dispersivity of the soil is discussed in Chapter 8. The effect of additives on the shrinkage limit of the soil with and without dispersing agent has been compared. The variation in shrinkage limit of the soil when treated with the additives was due to the different mechanisms involved in reducing the dispersivity by each additive. The effect on the unconfined compression strength of the soil treated with the additives with and without dispersing agent is also brought out in this chapter. It was noted that the dispersion exhibited through shrinkage limit test was lesser as compared to the percentage dispersivity exhibited through unconfined compression test. Hence it could be said that dispersion of the soil is due to loss of cohesion than volume change behavior. Also, the unconfined compression strength of the soils with respect to curing period is compared. The percentage dispersivity calculated through these tests is summarized and compared. With the help of this it could be said that to control the dispersivity of the soil, it is necessary to enhance the strength of the soil. The general summary and major conclusions drawn from the thesis are presented in Chapter 9.