# Browsing by Subject "Solute transport"

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Item Carbon dioxide storage in geologically heterogeneous formations(2013-12) Chang, Kyung Won; Hesse, Marc; Nicot, Jean-Philippe, 1958-Show more Geological carbon dioxide (CO₂) storage in deep geological formations can only lead to significant reductions in anthropogenic CO₂ emissions if large amounts of CO₂ can be stored safely. Determining the storage capacity, which is the volume of CO₂ stored safely, is essential to determine the feasibility of geological CO₂ storage. One of the main constraints for the storage capacity is the physical mechanisms of fluid flow in heterogeneous formations, which has not been studied sufficiently. Therefore, I consider two related problems: a) the evolution of injection-induced overpressure that determines the area affected by CO₂ storage and b) the rate of buoyant fluid flow along faults that determines the leakage of CO₂. I use a layered model of a sandstone reservoir embedded in mudrocks to quantify the increase in storage capacity due to dissipation of overpressure into the mudrocks. I use a model of a fault surface with flow barriers to constrain the reduction in the buoyancy-driven leakage flux across the fault. Using the layered model with injection at constant rate, I show that the pressure evolution in the reservoir is controlled by the amount of overpressure dissipated into ambient mudrocks. A main result of this study is that the pressure dissipation in a layered reservoir is controlled by a single dissipation parameter, M, that is identified here for the first time. I also show that lateral pressure propagation in the storage formation follows a power-law governed by M. The quick evaluation of the power-law allows a determination of the uncertainty in the estimate of the storage capacity. To reduce this uncertainty it is important to characterize the petrophysical properties of the mudrocks surrounding the storage reservoir. The uncertainty in mudrock properties due to its extreme heterogeneity or limited data available can cause large variability in these estimates, which emphasizes that careful characterization of mudrock is required for a reliable estimate of the storage capacity. The cessation of the injection operation will reduce overpressure near the injector, but regional scale pressure will continue to diffuse throughout the whole formation. I have been able to show that the maximum radius of the pressure plume in the post-injection period is approximately 3.5 times the radius of the pressure plume at the cessation of injection. Two aquifers can be hydraulically connected by a fault cutting across the intermediate aquitard. If the upper aquifer contains denser fluid, an exchange flow across the fault will develop. The unstable density stratification leads to a fingering pattern with localized zones of upwelling and downwelling along the fault. Due to the small volume of the fault relative to the aquifers, the exchange-flow will quickly approach a quasi steady state. If the permeability of the fault plane is homogeneous, the average number of the quasi-steady plume fingers, (nu), scales with the square root of the Rayleigh number Ra and the exchange flux measured by dimensionless convective flux, the Sherwood number, Sh, is a linear function of Ra. The dispersive flux perpendicular to the flow direction induces the formation of wider fingers and subsequently the less convective flux parallel to the flow direction. In the flow system with larger Ra, even the same increase in transverse dispersivity [alpha]T causes stronger impact of the mechanical dispersion on the vertical exchange flow so that (nu) and Sh reduce more with larger [alpha]T . Both measured characteristics, however, follow the same scaling for the non-dispersive homogeneous case by using a modified Rayleigh number, Ra*, considering the mechanical dispersion. The presence of flow barriers along the fault triggers unsteady exchange flow and subsequently controls the growth of the plume fingers. If the barriers are sufficiently wide to dominate the flow system, they create preferential pathways for exchange flow that determines the distribution of the quasi-steady fingers, and (nu) converges to a constant value. In addition, wider barriers induce substantial lateral spreading and enhance the efficiency of structural trapping, and reduce the exchange rate but still follows a linear relationship function of the effective Rayleigh number, Raeff , defined by the vertical effective permeability. This study is motivated by geological CO₂ storage in brine-saturated aquifer, but the effect of geological heterogeneity is also important in many other geological and engineering applications, in particular the risk assessment of the injection operations or the migration of hydrocarbons in tectonic-driven or hydraulically developed faults in reservoirs. Better understanding of fluid flow in geologically heterogeneous formations will allow more precise estimate of the reservoir capacity as well as more efficient operation of injection or production wells.Show more Item Investigation of local mixing and its influence on core scale mixing (dispersion)(2008-08) Jha, Raman Kumar; Bryant, Steven L.; Lake, Larry W.Show more Local displacement efficiency in miscible floods is significantly affected by mixing taking place in the medium. Laboratory experiments usually measure flow-averaged ("cup mixed") effluent concentration histories. The core-scale averaged mixing, termed as dispersion, is used to quantify mixing in flow through porous media. The dispersion coefficient has the contributions of convective spreading and diffusion lumped together. Despite decades of research there remain questions about the nature and origin of dispersion. The main objective of this research is to understand the basic physics of solute transport and mixing at the pore scale and to use this information to explain core-scale mixing behavior (dispersion). We use two different approaches to study the interaction between convective spreading and diffusion for a range of flow conditions and the influence of their interaction on dispersion. In the first approach, we perform a direct numerical simulation of pore scale solute transport (by solving the Navier Stokes and convection diffusion equations) in a surrogate pore space. The second approach tracks movement of solute particles through a network model that is physically representative of real granular material. The first approach is useful in direct visualization of mixing in pore space whereas the second approach helps quantify the effect of pore scale process on core scale mixing (dispersion). Mixing in porous media results from interaction between convective spreading and molecular diffusion. The converging-diverging flow around sand grains causes the solute front to stretch, split and rejoin. In this process the area of contact between regions of high and low solute concentrations increases by an order of magnitude. Diffusion tends to reduce local variations in solute concentration inside the pore body. If the fluid velocity is small, diffusion is able to homogenize the solute concentration inside each pore. On the other hand, in the limit of very large fluid velocity (or no diffusion) local mixing because of diffusion tends to zero and dispersion is entirely caused by convective spreading. Flow reversal provides insights about mixing mechanisms in flow through porous media. For purely convective transport, upon flow reversal solute particles retrace their path to the inlet. Convective spreading cancels and echo dispersion is zero. Diffusion, even though small in magnitude, causes local mixing and makes dispersion in porous media irreversible. Echo dispersion in porous media is far greater than diffusion and as large as forward (transmission) dispersion. In the second approach, we study dispersion in porous media by tracking movement of a swarm of solute particles through a physically representative network model. We developed deterministic rules to trace paths of solute particles through the network. These rules yield flow streamlines through the network comparable to those obtained from a full solution of Stokes' equation. In the absence of diffusion the paths of all solute particles are completely determined and reversible. We track the movement of solute particles on these paths to investigate dispersion caused by purely convective spreading at the pore scale. Then we superimpose diffusion and study its influence on dispersion. In this way we obtain for the first time an unequivocal assessment of the roles of convective spreading and diffusion in hydrodynamic dispersion through porous media. Alternative particle tracking algorithms that use a probabilistic choice of an out-flowing throat at a pore fail to quantify convective spreading accurately. For Fickian behavior of dispersion it is essential that all solute particles encounter a wide range of independent (and identically distributed) velocities. If plug flow occurs in the pore throats a solute particle can encounter a wide range of independent velocities because of velocity differences in pore throats and randomness of pore structure. Plug flow leads to a purely convective spreading that is asymptotically Fickian. Diffusion superimposed on plug flow acts independently of convective spreading causing dispersion to be simply the sum of convective spreading and diffusion. In plug flow hydrodynamic dispersion varies linearly with the pore-scale Peclet number. For a more realistic parabolic velocity profile in pore throats particles near the solid surface of the medium do not have independent velocities. Now purely convective spreading is non-Fickian. When diffusion is non-zero, solute particles can move away from the low velocity region near the solid surface into the main flow stream and subsequently dispersion again becomes asymptotically Fickian. Now dispersion is the result of an interaction between convection and diffusion and it results in a weak nonlinear dependence of dispersion on Peclet number. The dispersion coefficients predicted by particle tracking through the network are in excellent agreement with the literature experimental data. We conclude that the essential phenomena giving rise to hydrodynamic dispersion observed in porous media are (i) stream splitting of the solute front at every pore, thus causing independence of particle velocities purely by convection, (ii) a velocity gradient within throats and (iii) diffusion. Taylor's dispersion in a capillary tube accounts for only the second and third of these phenomena, yielding a quadratic dependence of dispersion on Peclet number. Plug flow in the bonds of a physically representative network accounts for the only the first and third phenomena, resulting in a linear dependence of dispersion upon Peclet number.Show more Item Modeling single-phase flow and solute transport across scales(2014-12) Mehmani, Yashar; Balhoff, Matthew T.Show more Flow and transport phenomena in the subsurface often span a wide range of length (nanometers to kilometers) and time (nanoseconds to years) scales, and frequently arise in applications of CO₂ sequestration, pollutant transport, and near-well acid stimulation. Reliable field-scale predictions depend on our predictive capacity at each individual scale as well as our ability to accurately propagate information across scales. Pore-scale modeling (coupled with experiments) has assumed an important role in improving our fundamental understanding at the small scale, and is frequently used to inform/guide modeling efforts at larger scales. Among the various methods, there often exists a trade-off between computational efficiency/simplicity and accuracy. While high-resolution methods are very accurate, they are computationally limited to relatively small domains. Since macroscopic properties of a porous medium are statistically representative only when sample sizes are sufficiently large, simple and efficient pore-scale methods are more attractive. In this work, two Eulerian pore-network models for simulating single-phase flow and solute transport are developed. The models focus on capturing two key pore-level mechanisms: a) partial mixing within pores (large void volumes), and b) shear dispersion within throats (narrow constrictions connecting the pores), which are shown to have a substantial impact on transverse and longitudinal dispersion coefficients at the macro scale. The models are verified with high-resolution pore-scale methods and validated against micromodel experiments as well as experimental data from the literature. Studies regarding the significance of different pore-level mixing assumptions (perfect mixing vs. partial mixing) in disordered media, as well as the predictive capacity of network modeling as a whole for ordered media are conducted. A mortar domain decomposition framework is additionally developed, under which efficient and accurate simulations on even larger and highly heterogeneous pore-scale domains are feasible. The mortar methods are verified and parallel scalability is demonstrated. It is shown that they can be used as “hybrid” methods for coupling localized pore-scale inclusions to a surrounding continuum (when insufficient scale separation exists). The framework further permits multi-model simulations within the same computational domain. An application of the methods studying “emergent” behavior during calcite precipitation in the context of geologic CO₂ sequestration is provided.Show more Item Outcrop-constrained flow and transport models of reflux dolomitization(2009-12) Garcia-Fresca, Beatriz, 1973-; Lucia, F. Jerry; Sharp, John Malcolm, Jr., 1944-Show more Two hydrogeologic models explore reflux dolomitization using two outcrop datasets at different scales to constrain transient boundary conditions and heterogeneous petrophysical properties. A platform-scale petrophysical model of the Permian San Andres Formation was built from outcrop and subsurface data following a reservoir modeling approach that preserves outcrop heterogeneity and incorporates a sequence stratigraphic framework. This model was used as input for hydrogeological simulations of hypersaline fluid flow and solute transport during the accumulation and compaction of the platform. Boundary conditions change over time, as relative sealevel fluctuations drive sedimentation, depositional environment migration, topographic gradients, and location, size and salinity of the brine source. The potential volume and distribution of dolomite formed is inferred by a magnesium mass-balance. The composite result of reflux events at various orders of stratigraphic hierarchy is a complex dolomite pattern that resembles that observed on San Andres outcrops. Dolostone bodies across the platform may be generated by different combinations of favorable conditions, including proximity to the brine source, zones of higher permeability, permeability contrasts, and latent reflux. A meter-scale reactive transport model of the Albian Upper Glen Rose Formation simulates deposition of three high-frequency cycles punctuated by three brine reflux events. The simulator determines flow, solute and reactive transport along the flow paths, revealing the spatial and temporal distribution of calcite dissolution, and precipitation of dolomite and sulfate. The model recreates fully and partially dolomitized cycles within the time and lithological constrains on Glen Rose outcrops. Our results show that the distribution of dolomite within a high-frequency cycle may be the net result of intercycle processes, whereby dolomitizing fluids sourced from younger cycles flow across stratigraphically significant boundaries. We also show that variations in dolomite abundance and the unfulfilled dolomitization potential control the contemporaneous propagation of multiple dolomite fronts and the coalescence of discrete dolomite bodies. Results show that reflux is an effective and efficient mechanism to dolomitize carbonate formations that progresses simultaneously with sediment accumulation. Dolomitization is the cumulative result of many short-lived reflux events, sourced in different locations and times, and amalgamation of successive dolostone bodies. This model contrasts with previous studies that approached dolomitization of a carbonate platform as a discrete reflux event and current interpretations that relate dolomite bodies to their most immediate stratigraphic surfaces.Show more Item Surface roughness of natural rock fractures : implications for prediction of fluid flow(2010-05) Slottke, Donald Timothy; Sharp, John Malcolm, Jr., 1944-; Ketcham, Richard A; Cardenas, M. Bayani; Laubach, Stephen E; Mace, Robert EShow more Where open, connected fractures are present, they dominate both fluid flow and transport of solutes, but the prediction of hydraulic and transport properties a priori has proven exceedingly difficult. A major challenge in predicting solute transport in fractured media is describing the physical characteristics of a representative surface that is appropriate to modeling. Fracture aperture, roughness, and channeling characteristics are important to predict flow and transport in hard rock terrains. In areas with little soil cover, fracture mapping can indicate areas or directions of greater permeability but not the magnitudes. Both cover and complex geology can limit mapping. Hand samples are generally available and upscaling from their properties would be highly beneficial. Assessing the impact of roughness on field-scale fluid flow through fractured media from samples of natural fractures on the order of 100cm² assumes a relationship between fracture morphology and discharge is either scale invariant or smoothly transformable. It has been suggested that the length scale that surface roughness significantly contributes to the discharge falls within the size of a typical hand sample, but few data exist to support extension of small-scale relationships to larger scales. I analyze the results of flow tests on a single fracture through a 60 x 30cm block of rhyolitic tuff. The results are compared with relationships of smaller samples in a similar tuffs and granites. The data are processed to yield regularly gridded surface elevations. Describing roughness as a ratio of surface area to footprint, variances of the roughnesses of surface covering equivalently sized square samples are plotted against sample size to determine if a representative surface exists. For specimens of fractures measuring up to 25 x 29cm, a 3.2 x 3.2cm sample of granite with an iron oxide/clay fracture skin yields a reasonable expression of the roughness of the entire surface. The number of data points included in a sample of this size transcends skin type, composition and grain/crystal size. The results suggest that the unmodified cubic law is valid for the range of gradients expected in the field using the geometric mean of areal aperture data to estimate hydraulic aperture. The data also indicate that fracture aperture is not well predicted by single aperture measurements or even by averaging along a particular scan line; three-dimensional laboratory analysis and/or field testing are required. There may be a suitable scale of data for upscaling fracture roughness on the order of 10cm². However, due to mismatch between top and bottom surfaces inherent in natural fractures, aperture samples are not consistent across the specimen and cannot be scaled. Upscaling of other factors, such as flow channeling, remain to be tested.Show more