Geological carbon dioxide (CO₂) capture and storage in geological formations has the potential to reduce anthropogenic emissions. The viability of technology depends on the long-term security of the geological CO₂ storage. Dissolution of CO₂ into the brine, resulting in stable stratification, has been identified as the key to long-term storage security. The dissolution rate determined by convection in the brine is driven by the increase of brine density with CO₂ saturation. Here we present a new analog laboratory experiment system to characterize convective dissolution in homogeneous porous medium. By understanding the relationship between dissolution and the Rayleigh number in homogeneous porous media, we can evaluate if convective dissolution occurs in the field and, in turn, to estimate the security of geological CO₂ storage fields. The large experimental assembly will allow us to quantify the relationship between convective dynamics and the Rayleigh number of the system, which could be essential to trapping process at Bravo Dome. A series of pictures with high resolution are taken to show the existence and movement of fingers of analog fluid. Also, these pictures are processed, clearly showed the concentration of analog fluid, which is essential to analyze the convective dissolution in detail. We measured the reduction in the convective flux due to hydraulic dispersion effect compared to that in homogeneous media, to determine if convective dissolution is an important trapping process at Bravo Dome. / text

The purpose of this dissertation is to establish a unified theory of porohyperelasticity with transport and growth and to demonstrate the capability of this theory using a finite element model developed in MATLAB. The theory of volumetric growth is combined with the theory of mixed porohyperelasticity with transport and swelling (MPHETS) to derive a new method that models growth of biological soft tissues. The conservation equations and constitutive equations are developed for both solid-only growth and solid-fluid growth. An axisymmetric finite element framework is introduced for the new theory of growing MPHETS (GMPHETS). To demonstrate the difference of the GMPHETS model from a traditional hyperelastic (HE) growth model, several finite element test problems with example growth laws are considered, including time-dependent, concentration-dependent, and stress-dependent growth. In particular, this work demonstrates that the solid-only growth of an MPHETS model of a stylized artery results in a more uniform hoop stress than in a HE model under solid-only growth for the same amount of growth time using the same growth law. This may have implications in the context of developing residual stresses in soft tissues under intraluminal pressure. To my knowledge, this is the first description of an MPHETS model with growth. The developed computational framework can be used together with novel in-vitro and in-vivo experimental approaches to identify the governing growth laws for various soft tissues.

Thermosolutal fluid flow has a strong influence on the evolution of solidification microstructures. While porous media theory and volume-averaged permeability relations give a basis to quantify these phenomena, traditional methods of permeability estimation used for random porous media fail to adequately characterize the full relation of microstructural morphology to volume-average permeability. Most significantly, the link between microstructural parameters and permeability is treated as a deterministic function at all scales, ignoring the variability inherent in porous media.The variation in permeability inherent to random porous media is investigated by the numerical solution of Stokes equations on an ensemble of porous media, which represent of many scales of sampling and morphological character. Based on volume-averaging and statistical treatment, the stochastic character of tensoral permeability in porous media is numerically investigated. Quantification of permeability variation and autocorrelation structure are presented as conditions, which future realistic stochastic permeability fields must respect.

Motivated by the reservoir engineering concept of the productivity index of a producing oil well in an isolated reservoir, we analyze a time dependent functional, diffusive capacity, on the solutions to initial boundary value problems for a parabolic equation. Sufficient conditions providing for time independent diffusive capacity are given for different boundary conditions. The dependence of the constant diffusive capacity on the type of the boundary condition (Dirichlet, Neumann or third-type boundary condition) is investigated using a known variational principle and confirmed numerically for various geometrical settings. An important comparison between two principal constant values of a diffusive capacity is made, leading to the establishment of criteria when the so-called pseudo-steady-state and boundary-dominated productivity indices of a well significantly differ from each other. The third type boundary condition is shown to model the thin skin effect for the constant wellbore pressure production regime for a damaged well. The questions of stabilization and uniqueness of the time independent values of the diffusive capacity are addressed. The derived formulas are used in numerical study of evaluating the productivity index of a well in a general three-dimensional reservoir for a variety of well configurations.

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Fluid flow process in fractured reservoirs is controlled primarily by the connectivity of fractures. The presence of fractures in these reservoirs significantly affects the mechanism of fluid flow. They have led to problems in the reservoir which results in early water breakthroughs, reduced tertiary recovery efficiency due to channeling of injected gas or fluids, dynamic calculations of recoverable hydrocarbons that are much less than static mass balance ones due to reservoir compartmentalization, and dramatic production changes due to changes in reservoir pressure as fractures close down as conduits. These often lead to reduced ultimate recoveries or higher production costs. Generally, modeling flow behavior and mass transport in fractured porous media is done using the dual-continuum concept in which fracture and matrix are modeled as two separate kinds of continua occupying the same control volume (element) in space. This type of numerical model cannot reproduce many commonly observed types of fractured reservoir behavior since they do not explicitly model the geometry of discrete fractures, solution features, and bedding that control flow pathway geometry. This inaccurate model of discrete feature connectivity results in inaccurate flow predictions in areas of the reservoir where there is not good well control. Discrete Fracture Networks (DFN) model has been developed to aid is solving some of these problems experienced by using the dual continuum models. The Discrete Fracture Networks (DFN) approach involves analysis and modeling which explicitly incorporates the geometry and properties of discrete features as a central component controlling flow and transport. DFN are stochastic models of fracture architecture that incorporate statistical scaling rules derived from analysis of fracture length, height, spacing, orientation, and aperture. This study is focused on developing a methodology for application of DFN to a shale gas reservoir and the practical application of DFN simulator (FracGen and NFflow) for fracture modeling of a shale gas reservoir and also studies the interaction of the different fracture properties on reservoir response. The most important results of the study are that a uniform fracture network distribution and fracture aperture produces the highest cumulative gas production for the different fracture networks and fracture/well properties considered.

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