The increasing concentration of CO_(2) has been linked to global warming and changes in climate. Geologic sequestration of CO_(2) in deep saline aquifers is a proposed greenhouse gas mitigation technology with potential to significantly reduce atmospheric emissions of CO_(2). Feasibility assessments of proposed sequestration sites require realistic and computationally efficient models to simulate the subsurface pressure response and monitor the injection process, and quantify the risks of leakage if there is any. This study investigates the possibility of obtaining closed form expressions for spatial distribution of CO_(2) injected in brine aquifers and gas reservoirs. Four new semi-analytical solutions for CO_(2) injection in brine aquifers and gas reservoirs are derived in this dissertation. Both infinite and closed domains are considered in the study. The first solution is an analysis of CO_(2) injection into an initially brine-filled infinite aquifer, exploiting self–similarity and matched asymptotic expansion. The second is an expanding to the first solution to account for CO_(2) injection into closed domains. The third and fourth solutions are analyzing the CO_(2) injection in infinite and closed gas reservoirs. The third and fourth solutions are derived using Laplace transform. The brine aquifer solutions accounted for both Darcyian and non-Darcyian flow, while, the gas reservoir solutions considered the gas compressibility variations with pressure changes. Existing analytical solutions assume injection under constant rate at the wellbore. This assumption is problematic because injection under constant rate is hard to maintain, especially for gases. The modeled injection processes in all aforementioned solutions are carried out under constant pressure injection at the wellbore (i.e. Dirichlet boundary condition). One major difficulty in developing an analytical or semi-analytical solution involving injection of CO_(2) under constant pressure is that the flux of CO_(2) at the wellbore is not known. The way to get around this obstacle is to solve for the pressure wave first as a function of flux, and then solve for the flux numerically, which is subsequently plugged back into the pressure formula to get a closed form solution of the pressure. While there is no simple equation for wellbore flux, our numerical solutions show that the evolution of flux is very close to a logarithmic decay with time. This is true for a large range of the reservoir and CO_(2) properties. The solution is not a formation specific, and thus is more general in nature than formation-specific empirical relationships. Additionally, the solution then can be used as the basis for designing and interpreting pressure tests to monitor the progress of CO_(2) injection process. Finally, the infinite domain solution is suitable to aquifers/reservoirs with large spatial extent and low permeability, while the closed domain solution is applicable to small aquifers/reservoirs with high permeability.

京都大学 / 新制・課程博士 / 博士(理学) / 甲第23675号 / 理博第4765号 / 新制||理||1683(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 坂上 貴之, 教授 泉 正己, 教授 國府 寛司 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

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Part I: The present work is to calculate dimensionless three-dimensional universal phase and lift force diagrams for a microbubble or pendant drop in a static liquid on a solid surface or orifice. Studying microbubble dynamics is important due to its controlling mass, momentum, energy and concentration transfer rates encountered in micro- and nano-sciences and technologies. In this work, dimensionless phase and force diagrams are presented by applying an equation for microbubble shape to accuracy of the second order of small Bond number provided by O¡¦Brien (1991). Two dimensionless independent parameters, Bond number and contact angle (or base radius), are required to determine dimensionless phase and force diagrams governing static and dynamic states of a microbubble. The phase diagram divides the microbubble surface into three regions, the apex to inflection, inflection to neck, and neck to the edge of microbubble. The growth, collapse, departure and entrapment of a microbubble on a surface thus can be described. The lift forces include hydrostatic buoyancy, difference in gas and hydrostatic pressures at the microbubble base, capillary pressure and surface tension resulted from variation of circumference. The force to attach the microbubble to solid surface is the surface tension resulted from variation of circumference, which is not accounted for in literature. Adjusting the base radius to control static and dynamic behaviors of a microbubble is more effective than Bond number. Part II: Controlling states and growth of a microscale bubble (or pendant drop) in a static liquid on a surface by introducing general phase diagrams is proposed. Microbubbles are often used to affect transport phenomena in micro- and nano-technologies. In this work, a general phase diagram is provided by applying a perturbation solution of Young-Laplace equation for bubble shape with truncation errors of the second power of small Bond number. The three-dimensional phase diagram for a given Bond number is uniquely described by the dimensionless radius of curvature at the apex, contact angle and base radius of the microbubble. Provided that initial and end states are chosen, adjusting two of them gives the desired states and growth, decay and departure of the bubble described by path lines in the phase diagram. A universal three-dimensional phase diagram for a microbubble is also introduced.