Quantitative characterization of the dynamics of water exchange fluxes between rivers and aquifers is necessary for water resources management, water quality, environment and ecology of the river-aquifer systems. The main uncertain factors for predicting river–aquifer exchange fluxes are aquifer and riverbed properties. In this study, we characterize the flux exchange dynamics between Brazos River Alluvium Aquifer and Brazos River, TX, USA, using alternative conceptual models. Six alternative conceptual models for the connection between the river and the aquifer, having varying aquifer lithology and river incision levels and incorporating processes such as river bed clogging and seepage face flow, are numerically modeled in HYDRUS 2D using small-scale, high-resolution transects across the river. Modeled results are tested against observed heads in three wells and finally a best-fit conceptual model is used to quantify river-aquifer flux exchange dynamics. Additionally we focused on how factors such as aquifer lithology, river channel incision, water table conditions, seepage face boundaries, and low-conductivity river-bed effect hydraulic head distribution and the corresponding flux exchange dynamics. Our results demonstrate that only a small portion of the aquifer close to the river channel is well-connected with the river and a major portion of the aquifer is disconnected. The proposed conceptual model predicts a) much frequent flux reversals (changes between gaining and losing conditions) and b) much smaller amount of recharge and discharges compared to that of the conceptual model which has been assumed by earlier studies; a reduction of 151% in recharge and 116% in discharges. These results suggest that the magnitude and dynamics of water flux exchange between the river and the aquifer are independent of the hydraulic gradients in the wider disconnected aquifer and are determined by the hydraulic gradients in the connected aquifer close to the river. The results also demonstrate that river-aquifer flux exchange is sensitive to aquifer lithology, river incision depth, and river-bed clogging. While different settings of aquifer lithology and river incision can produce very similar heads in the wider aquifer, the hydraulic head distribution close to the river and hence the river-aquifer flux exchange varies quite drastically from model to model. River-bed clogging decreases the magnitude of fluxes and effects hydraulic head in the aquifer, especially in the vicinity of the river channel, depending upon the gaining and losing river conditions. Furthermore, seepage face flow could be of the same order as that of flows through river-bed depending upon aquifer lithology and corresponding river incision depth.