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Surface acoustic waves (SAWs) on piezoelectric insulators can generate dynamic periodic potentials inside one-dimensional and two-dimensional materials. These periodic potentials have been utilized or proposed for various applications, including acoustoelectric charge pumping. In this study, we investigate acoustoelectric charge pumping in graphene with very low electrostatic disorder. By employing a graphite top gate on boron-nitride-encapsulated graphene, we adjust the graphene carrier concentration over a broad range, enabling us to examine the acoustoelectric signal in both mixed-carrier and single-carrier regimes. We discuss the benefits of h-BN-encapsulated graphene for charge pumping applications and introduce a model that describes the acoustoelectric signal across all carrier concentrations, including at the charge neutrality point. This quantitative model will support future SAW-enabled explorations of phenomena in low-dimensional materials and guide the design of novel SAW sensors.