Fundamental understanding of processes controlling geological carbon sequestration (GCS) requires flow and transport modeling in well-characterized aquifer sedimentary deposits. We use three-dimensional, heterogeneous models based on new field studies which incorporate the most important aspects of multiscale architecture in fluvial aquifers. In addition, we use the associated facies-dependent constitutive relations for both relative permeability and capillary pressure curves and their hysteresis. The novelty of this work is to evaluate how CO2 fate and transport is controlled by (1) the spatial organization, volume proportions, and connectivity of sedimentary facies types, (2) facies-dependent constitutive relations and their hysteretic behavior, and (3) presence and/or absence of dissolved components such as methane (CH4) in brine. Model results suggest that the amounts of snap-off and solubility trapping are enhanced by increasing the volume proportion and degree of connectivity of high-permeability facies types. Results also demonstrate that ignoring relative permeability hysteresis leads to underestimation of snap-off trapping and overestimation of solubility trapping. In contrast, neglecting capillary pressure hysteresis (i.e., non-hysteretic Pc) results in overestimation of snap-off trapping and underestimation of solubility trapping. If capillary pressure is totally neglected (i.e., Pc = 0), the amount of trapped CO2 by snap-off and dissolution are, respectively, overestimated and underestimated. Competitive CO2 and CH4 dissolution in brine results in exsolution of CH4 from the aqueous phase into the gaseous phase. Facies connectivity and constitutive relations are also critical for the transport of exsolved CH4. However, disregarding dissolved CH4 leads to overestimation of CO2 trapping capacities.