Carbon dioxide (CO2) sequestration is one of the most attractive methods to reduce the amount of CO2 in the atmosphere by injecting it into the geological formations. Furthermore, it is also an effective mechanism for enhanced oil recovery. Simulation of CO2 injection based on a suitable modeling is very important for explaining the fluid flow behavior of CO2 in a reservoir. Increasing of CO2 injection may cause a structural deformation of the medium. The structural deformation modeling in carbon sequestration is useful to evaluate the medium stability to avoid CO2 leakage to the atmosphere. Therefore, it is important to include such effect into the model. The purpose of this study is to simulate the CO2 injection in a reservoir. The numerical simulations of two-phase flow in homogeneous and heterogeneous porous media are presented. Also, the effects of gravity and capillary pressure are considered. IMplicit Pressure Explicit Saturation (IMPES) and IMplicit Pressure-Displacements and an Explicit Saturation (IMPDES) schemes are used to solve the problems under consideration. Various numerical examples were simulated and divided into two parts of the study. The numerical results demonstrate the effects of buoyancy and capillary pressure as well as the permeability value and its distribution in the domain. Some conclusions that could be derived from the numerical results are the buoyancy of CO2 is driven by the density difference, the CO2 saturation profile (rate and distribution) are affected by the permeability distribution and its value, and the displacements of the porous medium go to constant values at least six to eight months (on average) after injection. Furthermore, the simulation of CO2 injection provides intuitive knowledge and a better understanding of the fluid flow behavior of CO2 in the subsurface with the deformation effect of the porous medium.

ABSTRACT Modeling Diffusion and Buoyancy-Driven Convection with Application to Geological CO2 Storage Rebecca Allen Geological CO2 storage is an engineering feat that has been undertaken around the world for more than two decades, thus accurate modeling of flow and transport behavior is of practical importance. Diffusive and convective transport are relevant processes for buoyancy-driven convection of CO2 into underlying fluid, a scenario that has received the attention of numerous modeling studies. While most studies focus on Darcy-scale modeling of this scenario, relatively little work exists at the pore-scale. In this work, properties evaluated at the pore-scale are used to investigate the transport behavior modeled at the Darcy-scale. We compute permeability and two different forms of tortuosity, namely hydraulic and diffusive. By generating various pore ge- ometries, we find hydraulic and diffusive tortuosity can be quantitatively different in the same pore geometry by up to a factor of ten. As such, we emphasize that these tortuosities should not be used interchangeably. We find pore geometries that are characterized by anisotropic permeability can also exhibit anisotropic diffusive tortuosity. This finding has important implications for buoyancy-driven convection modeling; when representing the geological formation with an anisotropic permeabil- ity, it is more realistic to also account for an anisotropic diffusivity. By implementing a non-dimensional model that includes both a vertically and horizontally orientated 5 Rayleigh number, we interpret our findings according to the combined effect of the anisotropy from permeability and diffusive tortuosity. In particular, we observe the Rayleigh ratio may either dampen or enhance the diffusing front, and our simulation data is used to express the time of convective onset as a function of the Rayleigh ratio. Also, we implement a lattice Boltzmann model for thermal convective flows, which we treat as an analog for CO2 storage modeling. Our model contains the multiple- relaxation-time scheme and moment-based boundary conditions to avoid the numer- ical slip error that is associated with standard bounce-back. The model’s accuracy and robustness is demonstrated by an excellent agreement between our results and benchmark data for thermal flows ranging from Ra = 103 to 108. Our thermal model captures analogous flow behavior to that of CO2 through fluid-filled porous media, including the transition from diffusive transport to initiation and development of convective fingering.

>Magister Scientiae - MSc / This thesis deals with analysis and implementation of a positivity preserving numerical method for a vaccination model for the transmission dynamics of two HIVsubtypes in a given community. The continuous model is analyzed for stability and equilibria. The qualitative information thus obtained is used while designing numerical method(s). Three numerical methods, namely, Implicit Finite Difference Method (IFDM), Non-standard Finite Difference Method (NSFDM) and the Runge-Kutta method of order four (RK4), are designed and implemented. Extensive numerical simulation are carried out to justify theoretical outcomes.

Separation technologies with polymeric membranes are widely studied and have a wide range of applications. The membrane's heart is a dense selective layer whose permeability should strongly depend on the permeating species' properties. In turn, permeability depends on the diffusivity and solubility of the permeating species in the selective layer, which are considered intrinsic properties of the polymer forming the selective layer. When developing new membrane materials, the ultimate objective is to exceed the famous "upper bound" limit by achieving simultaneously higher selectivity and higher permeability. This objective is impossible without a reliable and accurate characterization method to determine the selective layer's intrinsic transport properties. The time-lag method is the most common membrane characterization technique, initially developed for polymeric membranes. However, as the membrane technology and material science advance, the selective layer structure becomes more complex and not limited to organic polymers. As a result, the time-lag method needs to be reviewed and adapted to these more complicated cases, which was the main objective of this thesis. Numerical simulation of dynamic gas permeation experiments is a powerful tool to examine different aspects of the time-lag method. Therefore, we have established a comprehensive variable-mesh finite-difference scheme, which was used throughout the thesis. It allowed us to investigate the effect of different random and resolution errors and an extrapolation error on the resulting time lag of an ideal membrane. We then considered more complex systems, particularly those of glassy polymers and mixed matrix membranes, to investigate the effect of different transport mechanisms on the results of dynamic and steady-state gas permeation experiments. In parallel, we also focused on developing a novel gas permeation system that would monitor dynamic gas permeation experiments based on pressure decay at the feed side. All the existing constant-volume gas permeation systems rely on monitoring pressure to rise at the membrane's permeate side. Although this work is still ongoing, we have made considerable progress. Among the numerous contributions made through this thesis, there are three of particular significance. We have developed an analytical model to predict mixed matrix membranes' relative permeability with the uniformly dispersed non-permeable fillers of different shapes. The model requires three structural parameters arising from the filler's shape and size, and it is superior to all existing analytical models, including the famous Maxwell model. We have also demonstrated that the diffusivity of mixed matrix membranes determined by the time-lag method depends on the number of layers of dispersed particles. In the limiting case of a single layer of uniformly impermeable fillers, it is possible for the diffusivity determined by the time-lag method to be greater than that of the host polymer, which might appear as counterintuitive in the absence of defects at the polymer-particle interface. In the case of glassy polymers, it is possible to observe an upward deviation from the steady-state flux, resulting from a non-instantaneous equilibrium between permeating species in Henry's and Langmuir adsorption sites.

abstract: I focus on algorithms that generate good sampling points for function approximation. In 1D, it is well known that polynomial interpolation using equispaced points is unstable. On the other hand, using Chebyshev nodes provides both stable and highly accurate points for polynomial interpolation. In higher dimensional complex regions, optimal sampling points are not known explicitly. This work presents robust algorithms that find good sampling points in complex regions for polynomial interpolation, least-squares, and radial basis function (RBF) methods. The quality of these nodes is measured using the Lebesgue constant. I will also consider optimal sampling for constrained optimization, used to solve PDEs, where boundary conditions must be imposed. Furthermore, I extend the scope of the problem to include finding near-optimal sampling points for high-order finite difference methods. These high-order finite difference methods can be implemented using either piecewise polynomials or RBFs. / Dissertation/Thesis / Doctoral Dissertation Mathematics 2019

京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第18416号 / 情博第531号 / 新制||情||94(附属図書館) / 31274 / 京都大学大学院情報学研究科複雑系科学専攻 / (主査)教授 磯 祐介, 教授 西村 直志, 教授 木上 淳, 講師 吉川 仁 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

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The steady flow method (SFM), most commonly used for permeability measurement in the laboratory, is not applicable for tight rocks, higher rank coals and coals under highly stressed condition because of the difficulty in measuring steady-state gas flowrates resulting from the tight rock structure of. However, accurate estimation of permeability of highly stressed coals is pivotal in coalbed methane (CBM) operations in order to precisely and effectively model and project long-term gas production. A fast and accurate permeability measurement technique is, therefore, required to investigate gas flow behavior of CBM reservoirs. The pulse-decay method (PDM) of permeability measurement is believed to be better suited for low-permeability rocks. In this study, application of the currently used pulse-decay laboratory permeability measurement techniques for highly stressed coals were evaluated. Considering the limitations of these techniques in permeability measurement of unconventional gas reservoirs, such as coal and gas shales, the conventional PDM was optimized by adjusting the experimental apparatus and procedures. Furthermore, the applicability of an optimized PDM was verified numerically and experimentally. This dissertation is composed of five chapters. To complete the research objectives as discussed above, it is necessary to have a profound understanding of the basic theories, such as, gas storage mechanism, gas migration, and permeability evolution during gas depletion in coalbed reservoirs. In Chapter 1, a brief discussion regarding the basic knowledge of reservoir properties and transport mechanisms is presented. The chapter also provides the appropriate background and rationale for the theoretical and experimental work conducted in this study. Chapter 2 presents the transient pressure-decay technique in permeability measurement of highly stressed coals and verifies the validity of Brace et al.’s solution (1968) by comparing it with Dicker and Smits’s solution (1988) and Cui et al.’s solution. The differences between these three solutions are discussed in detail. Based on the established permeability trends from these different solutions, a persuasive suggestion is presented for selection of the best alternative when testing coal permeability. Furthermore, permeability is regarded as a coupled parameter, resulting from the combined effects of mechanical compression and “matrix shrinkage” caused by desorption of gas. To isolate the role of gas desorption from the coupled result, a series of experiments were carried out under constant effective stress condition and a stress-dependent permeability trend was established. Chapter 3 proposes an optimized experimental design in order to improve the accuracy of the calculated permeability for sorptive rocks. In order to verify the optimized design theoretically, a modified mathematical model is presented and describes the one-dimensional fluid flow in porous media by a partial differential equation. The numerical solutions of the model are presented graphically to evaluate the fluid flow behavior in porous media. Finally, the validity of Brace et al.’s solution when testing sorptive rocks, without the need of consideration on the compressive storage and sorption effect, is elucidated. Chapter 4 demonstrates the efficiency and applicability of the optimized PDM through its direct application to experimental work designed to establish the permeability trend under best replicated in situ conditions. In this chapter, CO2 was used as the test fluid to profile and characterize the pulse decay plots due to its higher affinity towards coal than methane, and then establish the stress-dependent-permeability trend for highly-stressed CBM reservoirs. In this chapter, Brace et al.’s solution was also verified by comparing the laboratory data and computer simulated results obtained from the optimized mathematical model proposed in Chapter 3. The experimental work demonstrates that the optimized technique can be used for permeability tests of sorptive rocks without the need to carry out additional experimental work required to measure rock porosities and sorption isotherms. Finally, a summary and future research perspectives are presented in Chapter 5.

The modified Fiala model from Westin was implemented with conditions for circulatory shock and hypothermia. The purpose is to model Emergency Preservation and Resuscitation (EPR), a procedure for inducing hypothermia in patients. Cold tissue temperatures reduce metabolism exponentially, greatly extending the window of anaerobic metabolic activity before permanent deoxygenation damage. EPR in patients undergoing hypovolemic shock can preserve the patient until primary surgical care and blood transfusions are attainable., thereby increasing survival rates. The main applications of EPR are military in-situ stabilization for transit to clinical care and extending the survivability of patients requiring prolonged surgery before blood transfusion. The model explored in this paper seeks to model the tissue temperatures of the body while enduring circulatory shock and various options of cooling devices. Calibrating this model with already available data enables its use for getting preliminary results and design parameters for prototype cooling devices. The final objective of this research is to support the design of a cooling device that can induce sustained hypothermia in a field setting, while still being mobile enough for military and ambulance use.

This thesis has proposed a simplified model of corona discharge from an overhead wire struck by lightning for surge computations using the FDTD method. In the corona model, the progression of corona streamers from the wire is represented as the radial expansion of cylindrical conducting region around the wire. The validity of this corona model has been tested against experimental data. Then, its applications to lightning electromagnetic pulse computations have been reviewed. / 博士(工学) / Doctor of Philosophy in Engineering / 同志社大学 / Doshisha University