This work examines the effects of spatial heterogeneity in regulating Cr(Ⅵ)sorption under different geostatistical characteristics and spatial scale conditions.Previous flow-through experiments in heterogeneous columns of 0.1 meters have shown that sorption in heterogeneous media can be characterized by three effective quantities: sorption capacity(Csc,m),early-stage fast sorption rate(kc1),and late-stage slow sorption rate(kc2).Two-dimensional reactive transport models are developed by calibrating these data from these columns of different illite distribution patterns and permeability contrasts between illite and quartz zones.The models were further run in geostatistical fields of different permeability variance(σ2lnκ,0.2 and 4.5)and length scale(0.1 to 1.0 m)conditions to quantify their role in determining effective sorption capacity and kinetics.Simulation results indicate that in highly-connected columns with high permeability variance and long s,Cr(Ⅵ)-containing flow travels mostly through the high permeability,non-sorbing quartz zone.Sorption therefore occurs mostly at the illite-quartz interface.Sorption capacity and early fast rates(kc1)therefore depend strongly on the connectivity and properties that control advective transport of the column.At longer time scales,diffusive transport determines the late-stage slow rates(kc2)and the breakthrough tailing,which depend less on connectivity and more on the size of the low-permeability illite zones and transverse dispersivity αT.Compared to homogeneous columns of the same illite content,highly-connected patterns can reduce effective sorption capacity by up to a factor of 6.7,fast sorption rates by a factor of 25.0,and slow sorption rate by a factor of more than 2.0 orders of magnitude.As the domain length increases,the effects of spatial heterogeneities on sorption capacity and early stage fast sorption rates diminish due to longer length scales for mixing; these effects however persist for the late-stage slow sorption rates because of the long-time characteristic times associated with diffusive transport