Browsing by Subject "Fluid flow"

Now showing 1 - 9 of 9

Compression and permeability behavior of natural mudstones
(2011-12) Schneider, Julia, 1981-; Flemings, Peter Barry, 1960-; Mohrig, David; Cardenas, Meinhard B.; Day-Stirrat, Ruarri J.; Germaine, John T.
Mudstones compose nearly 70% of the volume of sedimentary basins, yet they are among the least studied of sedimentary rocks. Their low permeability and high compressibility contribute to overpressure around the world. Despite their fundamental importance in geologic processes and as seals for anthropogenic-related storage, a systematic, process-based understanding of the interactions between porosity, compressibility, permeability, and pore-size distribution in mudstones remains elusive. I use sediment mixtures composed of varying proportions of natural mudstone such as Boston Blue Clay or Nankai mudstone and silt-sized silica to study the effect of composition on permeability and compressibility during burial. First, to recreate natural conditions yet remove variability and soil disturbance, I resediment all mixtures in the laboratory to a total stress of 100 kPa. Second, in order to describe the systematic variation in permeability and compressibility with clay fraction, I uniaxially consolidate the resedimented samples to an effective stress equivalent to about 2 km of burial under hydrostatic conditions. Scanning electron microscope images provide insights on microstructure. My experiments illuminate the controls on mudstone permeability and compressibility. At a given porosity, vertical permeability increases by an order of magnitude for clay contents ranging from 59% to 34% by mass whereas compressibility reduces by half at a given vertical effective stress. I show that the pore structure can be described by a dual-porosity system, where one rock fraction is dominated by silt where large pores are present and the majority of flow occurs and the other fraction is dominated by clay where limited flow occurs. I use this concept to develop a coupled compressibility-permeability model in order to predict porosity, permeability, compressibility, and coefficient of consolidation. These results have fundamental implications for a range of problems in mudstones. They can be applied to carbon sequestration, hydrocarbon trapping, basin modeling, overpressure distribution and geometry as well as morphology of thrust belts, and an understanding of gas-shale behavior.
Fluid flow during low-[delta]¹⁸O skarn formation : insights from Empire Mountain, Mineral King, Sierra Nevada
(2017-05) Ramos, Evan Joseph; Barnes, Jaime Danielle; Hesse, Marc
A two-dimensional numerical simulation of oxygen isotope transport in the shallow crust has been developed to examine the mechanisms of fluid flow during the formation of skarns. The Empire Mountain skarn in Mineral King, Sierra Nevada -- the motivation of this study -- has recently been identified as a low-δ¹⁸O skarn and interpreted as indicating the presence surface fluids during the onset of its formation (D'Errico et al., 2012). Rapid and sporadic changes in δ¹⁸O values within a single garnet have been interpreted as alternation between meteoric and magmatic fluid during garnet growth. D'Errico et al. (2012) conclude that multiple events of hydrofracturing of existing rock created transient, high-permeability conduits in the shallow crust, providing a low-resistance pathway for surface fluids to reach skarn-forming depths (~2-5 km). However, hydrofracturing typically occurs during retrograde metamorphic conditions which conflicts with the hypothesized prograde hydrofracturing during the incipient formation of the Empire Mountain skarn. Given this discrepancy, the objectives of this study are twofold: to explore mechanisms that can explain (1) the existence of meteoric δ¹⁸O signatures at skarn-forming depths and (2) the rapid and sporadic changes in fluid δ¹⁸O values throughout skarn formation. Numerical simulations reveal three ways in which a meteoric fluid signature can exist at skarn-forming depths during the onset of skarn formation: (1) convection-driven drawdown of surface waters in uniform, high permeability country rock; (2) existence of a large permeability contrast in the surrounding rock (e.g., extensional faults) that entrains surface water to depth; and (3) existence of pore fluids in isotopic equilibrium with ¹⁸O-depleted minerals prior to the magmatic intrusion. Possibilities (1) and (2) are difficult to substantiate given limited knowledge of the once overlying stratigraphy whereas the third provides the simplest explanation. Large fluctuations in fluid oxygen isotope compositions are observed in all three scenarios. In our model, the largest fluctuations in δ¹⁸O values occur while garnet is thermodynamically stable, in areas nearest to the magmatic body, and downstream relative to the topography-driven flow field. However, low δ¹⁸O and δ¹³C values of carbonates at Empire Mountain indicate infiltration-driven fluid flow during metamorphism, likely caused by the ductile collapse of carbonate pore space followed by brecciation. Ultimately, even though there exist scenarios that demonstrably show the occurrence of low-δ¹⁸O skarns, future simulations must include rock deformation (i.e., ductile closure of pore space and hydrofracturing) and mineral reactions to gain further insight to how low-δ¹⁸O skarns incorporate fluids with meteoric oxygen isotope signatures.
Linear instability for incompressible inviscid fluid flows : two classes of perturbations
(2009-08) Thoren, Elizabeth Erin; Vishik, Mikhail
One approach to examining the stability of a fluid flow is to linearize the evolution equation at an equilibrium and determine (if possible) the stability of the resulting linear evolution equation. In this dissertation, the space of perturbations of the equilibrium flow is split into two classes and growth of the linear evolution operator on each class is analyzed. Our classification of perturbations is most naturally described in V.I. Arnold’s geometric view of fluid dynamics. The first class of perturbations we examine are those that preserve the topology of vortex lines and the second class is the factor space corresponding to the first class. In this dissertation we establish lower bounds for the essential spectral radius of the linear evolution operator restricted to each class of perturbations.
Machine learning applications for porous media
(2021-12-09) Estrada Santos, Javier Andres; Prodanovic, Masa; Pyrcz, Michael; DiCarlo, David; Lake, Larry; Lubbers, Nicholas
Understanding how fluids flow through permeable structures in the subsurface is paramount in the design and execution of projects for hydrocarbon extraction, CO₂ sequestration, and contaminant tracing in aquifers. The most important processes that impact fluid behavior of a field happen at the pore-scale. Therefore, these will be studied in detail throughout this dissertation. In particular, the main focus of this work is to estimate the permeability of 3D volumes. The permeability is arguably the most important property of a subsurface formation since it describes the ease for fluids to travel through a porous domain of interest. This, in turn, will control how fast a CO₂ plume will migrate, how much oil can be recovered from a reservoir, or when will a contaminant reach a certain region, among other relevant applications. This quantity can be computed via direct flow simulation, which provides accurate results, nevertheless, it is computationally very expensive. In particular, the simulation convergence time scales poorly as the domains become less porous or more heterogeneous. On the other hand, semi-analytical models that rely on averaged structural properties (i.e., porosity and tortuosity) have been proposed, but these properties only partly describe the domain, resulting in limited generalizability of these models. Alternatively, machine learning models have shown to be effective tools for finding complex relationships in structured data. These models have had great success at otherwise difficult tasks like natural language processing, video frame prediction, and semantic segmentation of natural scenes in real time. Nevertheless, the pore-scale world has remained vastly unexplored due to the the great effort needed to create labeled datasets, the complexity of obtaining and processing data, and the size of the 3D data arrays that concern subsurface applications. Having said that, the primary goal of this work is to show how to label datasets selectively, how to train models in cases where only a limited data is available, how to overcome the memory bottleneck of hardware, and how to bridge information from multiple scales. The goal of the models proposed in here is not to replace simulations or laboratory experiments, but to complement them. Throughout this dissertation, it is shown how a trained model can carry-out accurate predictions in a variety of domains. These models can provide good approximations, and can be specially useful when exploring a new reservoir, when tuning a segmentation, as initial conditions for a physics simulations, or when high performance computing resources are not available. It is our hope that the work presented here can be employed to build better and more accurate machine learning models that can advance the field of real-time data-driven alternatives for digital rock applications
Mechanical, failure and flow properties of sands : micro-mechanical models
(2011-05) Manchanda, Ripudaman; Olson, Jon E.; Sharma, Mukul M.
This work explains the effect of failure on permeability anisotropy and dilation in sands. Shear failure is widely observed in field operations. There is incomplete understanding of the influence of shear failure in sand formations. Shear plane orientations are dependent on the stress anisotropy and that view is confirmed in this research. The effect of shear failure on the permeability is confirmed and calculated. Description of permeability anisotropy due to shear failure has also been discussed. In this work, three-dimensional discrete element modeling is used to model the behavior of uncemented and weakly cemented sand samples. Mechanical deformation data from experiments conducted on sand samples is used to calibrate the properties of the spherical particles in the simulations. Orientation of the failure planes (due to mechanical deformation) is analyzed both in an axi-symmetric stress regime (cylindrical specimen) and a non-axi-symmetric stress regime (right cuboidal specimen). Pore network fluid flow simulations are conducted before and after mechanical deformation to observe the effect of failure and stress anisotropy on the permeability and dilation of the granular specimen. A rolling resistance strategy is applied in the simulations, incorporating the stiffness of the specimens due to particle angularity, aiding in the calibration of the simulated samples against experimental data to derive optimum granular scale elastic and friction properties. A flexible membrane algorithm is applied on the lateral boundary of the simulation samples to implement the effect of a rubber/latex jacket. The effect of particle size distribution, stress anisotropy, and confining pressure on failure, permeability and dilation is studied. Using the calibrated micro-properties, simulations are extended to non-cylindrical specimen geometries to simulate field-like anisotropic stress regimes. The shear failure plane alignment is observed to be parallel to the maximum horizontal stress plane. Pore network fluid flow simulations confirm the increase in permeability due to shear failure and show a significantly greater permeability increase in the maximum horizontal stress direction. Using the flow simulations, anisotropy in the permeability field is observed by plotting the permeability ellipsoid. Samples with a small value of inter-granular cohesion depict greater shear failure, larger permeability increase and a greater permeability anisotropy than samples with a larger value of inter-granular cohesion. This is estimated by the number of micro-cracks observed.
Pore fluid percolation and flow in ductile rocks
(2016-08) Ghanbarzadeh, Soheil; Prodanović, Maša; Hesse, Marc; Sepehrnoori, Kamy; Ebrom, Daniel; Bryant, Steven L; DiCarlo, David
Ductile rocks have capacity to deform in response to large strains without macroscopic fracturing. Such behavior may occur in rocks that did not undergo diagenesis, in weak materials such as rock salt or at greater depths in all rock types where higher temperatures promote crystal plasticity and higher confining pressures suppress brittle fracture (partially molten rocks). The pore network topology and fluid distribution in ductile rocks are governed by textural equilibrium. Therefore, textural equilibrium controls the distribution of the liquid phase in many naturally occurring porous materials such as partially molten rocks and alloys, salt-brine and ice-water systems. In this dissertation, we present a level set method to compute an implicit representation of the liquid-solid interface in textural equilibrium with space-filling tessellations of multiple solid grains in three dimensions. In ductile rocks, pore geometry evolves to minimize the solid-liquid interfacial energy while maintaining a constant dihedral angle, θ, at solid-liquid contact lines. Interfacial energy minimization with level set method is achieved by evolving the solid-liquid interface under surface diffusion to constant mean curvature surface. The liquid volume and dihedral angle constraints are added to the formulation using virtual convective and normal velocity terms. This results in a initial value problem for a system of nonlinear coupled PDEs governing the evolution of the level sets for each grain. A domain decomposition scheme is devised to restrict the computational domain of each grain to few grid points around the grain. The coupling between the interfaces is achieved in a higher level on the original computational domain. Our results show that the grain boundaries with the smallest area can be fully wetted by the pore fluid even for θ > 0. This was previously not thought to be possible at textural equilibrium and reconciles the theory with experimental observations. Even small anisotropy in the fabric of the porous medium allows the wetting of these faces at very low porosities, ϕ < 3%. Percolation and orientation of the wetted faces relative to the anisotropy of the fabric are controlled by θ. We have studied the fluid percolation and percolation thresholds in regular and irregular media. The results show that the pore space is connected at any non-zero porosity when θ ≤ 60°, and percolation threshold in an irregular media comprised of grains with different shapes and sizes is much higher than previously thought. Our results show that the pore network connectivity in ductile rocks is affected by the history of the systems and hysteresis determines the percolation when θ > 60°. We have also computed permeability of the pore networks in different porosities and dihedral angles for both regular and irregular media using Lattice Boltzmann method. Furthermore, we studied the effects of grain texture anisotropy on the permeability anisotropy. Until recent years, rock salt has been considered to be impermeable as it seems to contains and keep gas inclusions for long time. Increasing energy demand and necessity of producing hydrocarbon reservoir enclosed or touched by salt deposit and also urgent need of safe repository sites for high-level nuclear waste have brought attention to research and study the porosity and permeability of natural rock salt. Rock salt in sedimentary basins has long been considered to be impermeable and provides a seal for hydrocarbon accumulations in geological structures. The low permeability of static rock salt is due to a percolation threshold. However, deformation may be able to overcome this threshold and allow fluid flow. We confirm the percolation threshold in static experiments on synthetic salt samples with X-ray microtomography. We then analyze wells penetrating salt deposits in the Gulf of Mexico. The observed hydrocarbon distributions in rock salt require that percolation occurred at porosities considerably below the static threshold, due to deformation-assisted percolation. In general, static percolation thresholds may not always limit fluid flow in deforming environments. Here we use pore-scale simulations of texturally equilibrated pore networks to study the possibility of core formation by porous flow in planetesimals. Rapid core formation in early planetary bodies is required by geochemical data from extinct radionuclides. The most obvious mechanism for metal-silicate differentiation is the segregation of dense core forming melts by porous flow. However, experimental observations show that the texturally equilibrated metallic melt resides in isolated pockets that prevent percolation towards the center. The proposed hypothesis in this dissertation is that the porosities can be large enough to exceed percolation threshold and allow metalic melt drainge to center. The melt network remains interconnected as drainage reduces the porosity below the percolation threshold and only 1-2% is trapped. X-ray microtomography of lodran-like meteorite NWA 2993 provides evidence that volume fraction of metallic phases can exceed this percolation threshold. Lattice Boltzmann simulations show that the permeability during drainage remains significant. A model for metal-silicate differentiation by porous flow in a viscously compacting planetesimal is also proposed and shows that the efficient core formation requires early accretion and is completed almost 2 Myr after the onset of melting.
Pore-scale controls of fluid flow laws and the cappillary trapping of CO₂
(2013-08) Chaudhary, Kuldeep; Cardenas, Meinhard Bayani, 1977-; Bennett, Philip C. (Philip Charles), 1959-
A pore-scale understanding of fluid flow underpins the constitutive laws of continuum-scale porous media flow. Porous media flow laws are founded on simplified pore structure such as the classical capillary tube model or the pore-network model, both of which do not include diverging-converging pore geometry in the direction of flow. Therefore, modifications in the fluid flow field due to different pore geometries are not well understood. Thus this may translate to uncertainties on how flow in porous media is predicted in practical applications such as geological sequestration of carbon dioxide, petroleum recovery, and contaminant’s fate in aquifers. To fill this gap, we have investigated the role of a spectrum of diverging-converging pore geometries likely formed due to different grain shapes which may be due to a variety of processes such as weathering, sediment transport, and diagenesis. Our findings describe the physical mechanisms for the failure of Darcy’s Law and the characteristics of Forchheimer Law at increasing Reynolds Number flows. Through fundamental fluid physics, we determined the forces which are most responsible for the continuum-scale porous media hydraulic conductivity (K) or permeability. We show that the pore geometry and the eddies associated therein significantly modify the flow field and the boundary stresses. This has important implications on mineral precipitation-dissolution and microbial growth. We present a new non-dimensional geometric factor β, a metric for diverging-converging pore geometry, which can be used to predict K. This model for K based on β generalizes the original and now widely-used Kozeny (1927) model which was based on straight capillary tubes. Further, in order to better quantify the feasibility of geological CO2 sequestration, we have conducted laboratory fluid flow experiments at reservoir conditions to investigate the controls of media wettability and grain shapes on pore-scale capillary trapping. We present experimental evidence for the snap-off or formation of trapped CO2 ganglion. The total trapping potential is found to be 15% of porosity for a water-wet media. We show that at the pore-scale media wettability and viscous-fingering play a critical role in transport and trapping of CO2. Our investigations clearly show that that in single-phase flow pore geometry significantly modifies pore-scale stresses and impacts continuum-scale flow laws. In two-phase flows, while the media wettability plays a vital role, the mobility ratio of CO2 - brine system significantly controls the CO2 capillary trapping potential- a result which should be taken into consideration while managing CO2 sequestration projects.
Simulation of UV nanoimprint lithography on rigid and flexible substrates
(2016-12) Jain, Akhilesh; Bonnecaze, R. T. (Roger T.); Sreenivasan, S.V.; Willson, C. Grant; Schunk, P. Randall; Ganesan, Venkat
Nanoimprint lithography (NIL) is a low cost, high throughput process used to replicate sub-20 nm feature from a patterned template to a rigid or flexible substrate. Various configurations for NIL are analyzed and classified based on type of template and substrate. The steps involved in pattern transfer using roller template based NIL are identified and models to study these steps are proposed. Important process parameters such as maximum web speed possible, required UV intensity, minimum droplet size and pitch and required force on the roller are calculated. The advantages, disadvantages and optimal process window for the different configurations are identified. Droplet spreading is simulated in NIL with rigid substrates in order to study the effect of droplet size, droplet placement error, gas diffusion and template pattern on throughput and defectivity. Square arrangement is found to be the optimum arrangement for achieving minimum throughput. Large droplet-free regions on the substrate edge and error in droplet placement error have significant impact on the throughput. A fluid flow model with average flow permeability is presented to account for flow in the template patterns. Optimum droplet dispensing for multi-patterned templates is achieved by distributing droplet volume according to local filling requirements. Non-fill defects in NIL are classified into pocket, edge and channel defects. A model to predict the size of non-fill defects based on imprint time and droplet size is presented. Defect characterization is presented for various pattern-types. A model is presented to determine the time required for the encapsulated gas to diffuse into the resist. The coupled fluid-structure interaction in NIL with flexible substrate is studied by simulating the web deformation as the droplet spreads on the substrate. It is found that the flexible substrate can be modeled as a membrane due to the lack of rigidity. RLT variation reduces as the number of droplets or the web tension increases. For the magnitude of RLT variation, thinner residual layers require higher web tension. The position of the template on the substrate is important and template positioned at the corner of the substrate is found to provide the least RLT variation.
Understanding fluid flow in rough-walled fractures using x-ray microtomography images
(2015-08) Tokan-Lawal, Adenike O.; Eichhubl, Peter; Prodanović, Maša; Cardenas, M. Bayani; Fisher, William L
Natural fractures provide fluid flow pathways in otherwise low permeability reservoirs. These fractures are usually lined or completely filled with mineral cements. The presence of these cements causes very rough fracture walls that can constrict flow and hinder the connectivity between the fracture and matrix/fracture pores thereby reducing porosity, permeability and matrix/fracture transfer. In order to accurately predict fluid transport in the unconventional reservoirs, I study the influence of diagenesis (cementation and compaction in particular) and fracture roughness on flow in artificial (fractured polyethylene) and naturally fractured carbonate (Niobrara formation outcrop) and tight gas sandstones (Torridonian outcrop and Travis Peak reservoir in particular). X-ray microtomography imaging provides information on fracture geometry. Image analysis and characterization of the connectivity and geometric tortuosity of the pore space and individual fluid phases at different saturations, is performed via ImageJ and 3DMA Rock software. I also use a combination of the level-set-method-based progressive-quasistatic algorithm (LSMPQS software), and lattice Boltzmann simulation (Palabos software) to characterize the capillary dominated displacement properties and the relative permeability of the naturally cemented fractures within. Finally, I numerically investigate the effect of (uniform) cementation on the fracture permeability as well as the tortuosity of the pore space and the capillary pressure-water saturation (Pc-Sw) relationship in the Niobrara. Permeability estimates in the different formations vary by several orders of magnitude with the different correlations that currently exist in the literature for all samples studied. The presence of cements increases the geometric tortuosity of the pore space and capillary pressure while reducing the permeability and porosity. Contrary to our expectation, the tortuosity of either wetting or non-wetting phase and their respective relative permeabilities show no clear correlation. Overall, pore scale methods provide an insight to flow characteristics in rough walled fractures at micron scale that are not well represented by existing correlations. The measured properties can be used as input in reservoir simulators.