This work examines the influence of initial (i.e. post drainage) nonwetting (NW) fluid topology on total residual (i.e. after imbibition) NW phase saturation. Brine and air (used as a proxy for supercritical CO2) flow experiments were performed on Bentheimer sandstone; results were quantified via imaging with X-ray computed microtomography (X-ray CMT), which allows for three dimensional, non-destructive, pore-scale analysis of the amount, distribution, and connectivity of NW phase fluid within the sandstone cores. In order to investigate the phenomenon of fluid connectivity and how it changes throughout flow processes, the Bentheimer sandstone results are compared to previously collected X-ray CMT data from similar experiments performed in a sintered glass bead column, a loose packed glass bead column, and a column packed with crushed tuff. This allows us to interpret the results in a broader sense from the work, and draw conclusions of a more general nature because they are not based on a single pore geometry. Connectivity is quantified via the normalized Euler number of the NW fluid phase; the Euler number of a particular sample is normalized by the maximum connectivity of the media, i.e. the Euler number of the system at 100% NW phase saturation. General connectivity-saturation relationships were identified for the various media. In terms of trapping, it was found that residual NW phase trapping is dependent on initial (i.e. post-drainage) NW phase connectivity as well as imbibition capillary number for the Bentheimer sandstone. Conversely, the sintered glass bead column exhibited no significant relationship between trapping and NW topology.These findings imply that for a CO2 sequestration scenario, capillary trapping is controlled by both the imbibition capillary number and the initial NW phase connectivity: as capillary number increases, and the normalized initial Euler number approaches a value of 1.0, capillary trapping is suppressed. This finding is significant to CO2 sequestration, because both the drainage (CO2 injection) and imbibition (subsequent water injection or infiltration) processes can be engineered in order to maximize residual trapping within the porous medium. Based on the findings presented here, we suggest that both the Euler number-saturation and the capillary number-saturation relationships for a given medium should be considered when designing a CO2 sequestration scenario.