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Global warming and greenhouse gas (GHG) emissions have recently become the significant focus of engineering research. The geological sequestration of greenhouse gases such as carbon dioxide (CO2) is one approach that has been proposed to reduce the greenhouse gas emissions and slow down global warming. Geological sequestration involves the injection of produced CO2 into subsurface formations and trapping the gas through many geological mechanisms, such as structural trapping, capillary trapping, dissolution, and mineralization. While some progress in our understanding of fluid flow in porous media has been made, many petrophysical phenomena, such as multi-phase flow, capillarity, geochemical reactions, geomechanical effect, etc., that occur during geological CO2 sequestration remain inadequately studied and pose a challenge for continued study. It is critical to continue to research on these important issues. Numerical simulators are essential tools to develop a better understanding of the geologic characteristics of brine reservoirs and to build support for future CO2 storage projects. Modeling CO2 injection requires the implementation of multiphase flow model and an Equation of State (EOS) module to compute the dissolution of CO2 in brine and vice versa. In this study, we used the Integrated Parallel Accurate Reservoir Simulator (IPARS) developed at the Center for Subsurface Modeling at The University of Texas at Austin to model the injection process and storage of CO2 in saline aquifers. We developed and implemented new petrophysical models in IPARS, and applied these models to study the process of CO2 sequestration. The research presented in this dissertation is divided into three parts. The first part of the dissertation discusses petrophysical and computational models for the mechanical, geological, petrophysical phenomena occurring during CO2 injection and sequestration. The effectiveness of CO2 storage in saline aquifers is governed by the interplay of capillary, viscous, and buoyancy forces. Recent experimental data reveals the impact of pressure, temperature, and salinity on interfacial tension (IFT) between CO2 and brine. The dependence of CO2-brine relative permeability and capillary pressure on IFT is also clearly evident in published experimental results. Improved understanding of the mechanisms that control the migration and trapping of CO2 in the subsurface is crucial to design future storage projects for long-term, safe containment. We have developed numerical models for CO2 trapping and migration in aquifers, including a compositional flow model, a relative permeability model, a capillary model, an interfacial tension model, and others. The heterogeneities in porosity and permeability are also coupled to the petrophysical models. We have developed and implemented a general relative permeability model that combines the effects of pressure gradient, buoyancy, and capillary pressure in a compositional and parallel simulator. The significance of IFT variations on CO2 migration and trapping is assessed. The variation of residual saturation is modeled based on interfacial tension and trapping number, and a hysteretic trapping model is also presented. The second part of this dissertation is a model validation and sensitivity study using coreflood simulation data derived from laboratory study. The motivation of this study is to gain confidence in the results of the numerical simulator by validating the models and the numerical accuracies using laboratory and field pilot scale results. Published steady state, core-scale CO2/brine displacement results were selected as a reference basis for our numerical study. High-resolution compositional simulations of brine displacement with supercritical CO2 are presented using IPARS. A three-dimensional (3D) numerical model of the Berea sandstone core was constructed using heterogeneous permeability and porosity distributions based on geostatistical data. The measured capillary pressure curve was scaled using the Leverett J-function to include local heterogeneity in the sub-core scale. Simulation results indicate that accurate representation of capillary pressure at sub-core scales is critical. Water drying and the shift in relative permeability had a significant impact on the final CO2 distribution along the core. This study provided insights into the role of heterogeneity in the final CO2 distribution, where a slight variation in porosity gives rise to a large variation in the CO2 saturation distribution. The third part of this study is a simulation study using IPARS for Cranfield pilot CO2 sequestration field test, conducted by the Bureau of Economic Geology (BEG) at The University of Texas at Austin. In this CO2 sequestration project, a total of approximately 2.5 million tons supercritical CO2 was injected into a deep saline aquifer about ~10000 ft deep over 2 years, beginning December 1st 2009. In this chapter, we use the simulation capabilities of IPARS to numerically model the CO2 injection process in Cranfield. We conducted a corresponding history-matching study and got good agreement with field observation. Extensive sensitivity studies were also conducted for CO2 trapping, fluid phase behavior, relative permeability, wettability, gravity and buoyancy, and capillary effects on sequestration. Simulation results are consistent with the observed CO2 breakthrough time at the first observation well. Numerical results are also consistent with bottomhole injection flowing pressure for the first 350 days before the rate increase. The abnormal pressure response with rate increase on day 350 indicates possible geomechanical issues, which can be represented in simulation using an induced fracture near the injection well. The recorded injection well bottomhole pressure data were successfully matched after modeling the fracture in the simulation model. Results also illustrate the importance of using accurate trapping models to predict CO2 immobilization behavior. The impact of CO2/brine relative permeability curves and trapping model on bottom-hole injection pressure is also demonstrated.