Geostatistical methods based on two-point spatial-bivariate statistics have been used to model heterogeneity within computational studies of the dispersion of contaminants in groundwater reservoirs and the trapping of CO2 in geosequestration reservoirs. The ability of these methods to represent fluvial architecture, commonly occurring in such reservoirs, has been questioned. We challenged a widely used two-point spatial-bivariate statistical method to represent fluvial heterogeneity in the context of representing how reservoir heterogeneity affects residual trapping of CO2 injected for geosequestration. A more rigorous model for fluvial architecture was used as the benchmark in these studies. Both the geostatistically generated model and the benchmark model were interrogated, and metrics for the connectivity of high-permeability preferential flow pathways were quantified. Computational simulations of CO2 injection were performed, and metrics for CO2 dynamics and trapping were quantified. All metrics were similar between the two models. The percent of high-permeability cells in spanning connected clusters (percolating clusters) was similar because percolation is strongly dependent upon proportions, and the same proportion of higher permeability cross-strata was specified in generating both models. The CO2 plume dynamics and residual trapping metrics were similar because they are largely controlled by the occurrence of percolating clusters. The benchmark model represented more features of the fluvial architecture and, depending on context, representing those features may be quite important, but the simpler geostatistical model was able to adequately represent fluvial reservoir architecture within the context and within the scope of the parameters represented here.