Carbon capture and storage (CCS) has been identified as the only climate mitigation option that can significantly reduce anthropogenic CO2 emissions while allowing continued use of fossil fuels for electricity generation and other industrial processes. CCS involves permanent sequestration of the CO2 captured from burning of fossil fuels into deep geologic formations. This dissertation studies the two-phase flow dynamics of geologic CO 2 sequestration, as well as other subsurface fluid injections, including acid gas injection, liquid waste disposal and enhanced oil recovery; and develops a series of computational multiphase flow models with a broad range of complexity to understand and predict injection and migration of the various kinds of fluid injections in the subsurface.;Chapter 2 studies the axisymmetric flows generated from injection of one fluid into a horizontal confined porous medium originally filled with another fluid using the reduced-order vertical equilibrium and sharp interface assumptions, where four asymptotic analytical solutions and an associated flow regime diagram distinguishing the different solutions are obtained. Chapter 3 identifies the kinds of solutions appropriate for practical CO2 injection projects as well as other subsurface fluid injection applications. The analytical solutions and the flow regime diagram provide a simple guidance tool for expected behaviors of the different injection operations.;Chapters 4 and 5 report novel multiscale numerical algorithms and a range of vertically-integrated models that can model the two-phase flow dynamics of CO2 and brine in both homogeneous and layered heterogeneous geologic formations. The capability to capture the additional two-phase flow dynamics in the vertical dimension, while maintaining much of the computational advantages of the conventional vertical equilibrium models makes these multiscale models very attractive for computational studies of large-scale CO2 storage systems.;Chapter 6 highlights some interesting extensions to more advanced models from the multiscale algorithm developed in Chapters 4 and 5. The first direction of extension is a set of hybrid vertically-integrated multi-layer and multi-dimensional models for CO2 sequestration in geologic formations with complex geologic structures and other energy and environment systems involving subsurface fluid injection. The second direction of extension is a set of vertically-integrated dual-porosity dual-permeability models for modeling of geologic CO2 sequestration in fractured reservoirs.
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