Acoustic charge transport devices in GaAs are charge-coupled devices that typically transport charge at the velocity of sound. However, charge transport can be temporarily inhibited by electrical barriers in the transport channel, a process known as charge storage. In this paper the fundamental properties of two methods of charge storage, single-packet and double-packet, are investigated and compared using theory and experiments. A 1-D storage model is developed which provides insight into the dynamics of the charge storage process. The impact of charge storage on device frequency response is analyzed. Storage capacity is experimentally characterized as a function of storage voltage. The key factors that limit storage capacity are found to be intercell diffusion, surface charge extraction, barrier transition times, and delay-line charge capacity. Furthermore, double-packet storage has been found to provide higher storage capacity with less storage voltage than single-packet storage.