Browsing by Subject "Longitudinal dispersion"
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Item Modeling single-phase flow and solute transport across scales(2014-12) Mehmani, Yashar; Balhoff, Matthew T.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.Item Scale-up of dispersion for simulation of miscible displacements(2013-05) Adepoju, Olaoluwa Opeoluwa; Lake, Larry W.; Johns, Russell T.Dispersion has been shown to degrade miscibility in miscible displacements by lowering the concentration of the injected solute at the displacement fronts. Dispersion can also improve oil recovery by increasing sweep efficiency. Either way, dispersion is an important factor in understanding miscible displacement performance. Conventionally, dispersion is measured in the laboratory by fitting the solution of one-dimensional convection-dispersion equation (CDE) to the effluent concentration from a core flood. However dispersion is anisotropic and mixing occurs in both longitudinal and transverse directions. This dissertation uses the analytical solution of the two-dimensional CDE to simultaneously determine longitudinal and transverse dispersion. The two-dimensional analytical solution for an instantaneous finite volume source is used to investigate anisotropic mixing in miscible displacements. We conclude that transverse mixing becomes significant with large a concentration gradient in the transverse direction and significant local variation in flow directions owing to heterogeneity. We also utilized simulation models similar to Blackwell's (1962) experiments to determine transverse dispersion. This model coupled with the analytical solution for two-dimensional CDE for continuous injection source is used to determine longitudinal and transverse dispersivity for the flow medium. The validated model is used to investigate the effect of heterogeneity and other first contact miscible (FCM) scaling groups on dispersion. We derive the dimensionless scaling groups that affect FCM displacements and determine their impact on dispersion. Experimental design is used to determine the impact and interactions of significant scaling groups and generate a response surface function for dispersion based on the scaling groups. The level of heterogeneity is found to most significantly impact longitudinal dispersion, while transverse dispersion is most significantly impacted by the dispersion number. Finally, a mathematical procedure is developed to use the estimated dispersivities to determine a-priori the maximum grid-block size to maintain an equivalent level of dispersion between fine-scale and upscaled coarse models. Non-uniform coarsening schemes is recommended and validated for reservoir models with sets of different permeability distributions. Comparable sweep and recovery are observed when the procedure was extended to multi-contact miscible (MCM) displacements.Item Scaling of solutal convection in porous media(2017-12-08) Liang, Yu, active 21st century; DiCarlo, David Anthony, 1969-; Hesse, Marc; Lake, Larry; Mohanty, Kishore; Balhoff, MatthewConvective dissolution trapping is an important mechanism for CO₂ mitigation because of its high security and long-term storage capacity. This process is a problem of solutal convection in porous media, which is a classic example of symmetry breaking and pattern formation. The convective solute flux and geometry of the convective pattern are thought to be controlled by the molecular Rayleigh number, Raₘ, i.e., the ratio of the buoyant driving forces over diffusive dissipation. The dimensionless convective solute flux, Sh (Sherwood number), is thought to increase with Raₘ approximately linearly, as Sh ~ Raₘ. The spacing of the convective fingers, δ, relative to the domain height, H, is thought to decrease approximately as [mathematical equation]. However, there is little experimental verification of these fundamental scaling laws for solutal convection in porous media. To understand the controlling physics of CO₂ convective dissolution in aquifers and verify relevant fundamental scaling laws, I conduct convective dissolution experiments using analog fluids in a porous medium. By changing the controlling parameters, including permeability and maximum density difference, corresponding convective velocity, dissolution flux, and finger pattern are measured for each combination. The experimental results shows that these fundamental scaling laws do not hold for the experiments in porous media composed of glass beads. Instead, I observe that the dissolution flux levels off as Raₘ increases and that the finger spacing increases rather than decreases with increasing Raₘ. The classic scaling analysis breaks down because it does not consider the dominant dissipative mechanism in porous media, mechanical dispersion. Its influence on convection is captured by a dispersive Rayleigh number, Ra [subscript d] = H / αT, where αT is the transverse dispersivity. In experimental studies, dispersion dominates molecular diffusion, i.e., Ra [subscript d] ≤ Raₘ and therefore selects the finger spacing. Increasing the bead size of the porous medium increases Raₘ but decreases Ra [subscript d], leading to a coarsening of the convective pattern. The dissolution flux is controlled by Raₘ, which captured the buoyant driving force in the convection. However, the inherent anisotropy of mechanical dispersion leads to an asymmetry in the convective pattern that eventually limits the dissolution flux in the high Raₘ limit, resulting in the breakdown of the classic convective solute flux scaling. This anisotropy induced asymmetry and corresponding flux reduction are verified by a numerical simulation study. The results show that mechanical dispersion, which was ignored before, plays an important role in quantifying solutal convection in porous media. Since dispersivity generally increases with the scale of observations, knowledge obtained from the counter-intuitive results can be applied to predict mass transfer in large-scale applications such as CO₂ convective dissolution storage in aquifers.