The stability of residually trapped CO2 is often taken for granted in the simulation studies used for predicting the long-term fate of CO2 in geological storage reservoirs. Ostwald ripening is one of the mechanisms that could potentially remobilize residually trapped CO2. This mechanism would cause the gradual growth of ganglia with low capillary pressures at the expense of ganglia with higher capillary pressures. The growth of ganglia becomes an issue if the ganglia start expanding in the vertical direction. In porous media, capillary pressure at the top of a column of gas is directly related to the column height. Above a critical height, the capillary pressure at the top of the column could overcome the capillary entry pressure of the pores directly above it, and induce gravitational remobilization. Capillary heterogeneities at the pore scale are known to affect large-scale migration of gas plumes however. Ostwald ripening will be driven by differences in capillary pressure between ganglia, and subsequent diffusion of dissolved CO2 through the aqueous phase. In a bulk liquid medium, a bubble of gas is observed to be spherical. The capillary pressure of a spherical bubble of gas is inversely proportional to the bubble radius. In porous media on the other hand, the gas phase (observable through microtomographic imaging) takes the form of ganglia with complicated shapes and sizes. Capillary pressures of individual gas ganglia are thought to depend not on total ganglion volume, but rather on pore geometry and topology. A stable equilibrium where disconnected ganglia of different sizes share the same capillary pressure can be imagined. Critical questions relate to understanding and measuring the distribution of capillary pressure in isolated, disconnected ganglia, as well as studying their evolution in time. The goal of this study is therefore two-fold. We develop reliable methods to estimate the capillary pressure distributions for populations of disconnected ganglia of gases that are trapped during imbibition experiments in sandstones. Multi-resolution X-ray microtomography datasets from air-water spontaneous imbibition experiments in sintered glass beads and sandstone samples were acquired at the Advanced Light Source, in the Lawrence Berkeley National Laboratory. A series of computational techniques to process microtomography images; estimate curvature at the interface between two immiscible fluids; and then link these curvature estimates to the capillary pressures of the ganglia were developed based on these data sets. The work flow we develop allows us to estimate curvature distributions for disconnected gas ganglia and assess the reliability of the estimates. Pore structure as well as resolution are found to have a significant impact on curvature estimation. The capillary pressures of disconnected ganglia are also found to be controlled by neighboring pore throat radii. The capillary pressure at different locations on interface of a single ganglion is found to be similar, such that the average capillary pressure for a ganglion is well defined and displays little variability. The distribution of the average capillary pressures for disconnected ganglia is quantified in the different samples and across samples in order to assess the potential for Ostwald Ripening. A second research effort presented in this report focuses on simulating the evolution of multi-ganglia systems governed by ripening mechanisms in porous media. Using reduced dimension representations of the pore space, we study evolution in the context of simple physical laws to find equilibrium positions and guide physical intuition. The final equilibrium situation as well the time scales for evolution are found to be highly dependent on system initialization as well as on pore structure. The simulations also highlight the different evolution regimes of a multi-ganglia system in the bulk and porous medium settings.