Underground salt cavern gas storage is the best choice for the production peak adjustment and storage of natural gas, and is a basic means to ensure the safe supply of natural gas. However, in the process of these caverns dissolving due to water injection, argillaceous insoluble sediments in the salt layer will fall to the bottom of the cavity and expand, occupying a large amount of the storage capacity and resulting in the reduction of the actual gas storage space. Effectively reducing the volume of sediments at the bottom of the cavity is a potential way to expand the storage capacity of the cavity. In this study, a method to reduce the volume of argillaceous insoluble sediments with particle sizes ranging from 10 mesh to 140 mesh, via a chemical shrinkage agent, has been proposed. Firstly, the inorganic polymer shrinkage agent PAC30 was synthesized, and then a set of dynamic shrinkage evaluation methods was established to evaluate the influence of temperature, particle size, concentration, and other factors on the shrinkage performance. Finally, by means of a scanning electron microscope (SEM), the Zeta potential, and static adsorption experiments, the mechanism of the interaction between PAC30 and cavity-bottom sediments was described and verified in detail. The experimental results show that the optimal concentration of PAC30 for dynamic shrinkage is 20 ppm. The shrinkage performance of PAC30 decreases with an increase in temperature, and the smaller the particle size of the insoluble sediments, the worse the shrinkage performance. According to the adsorption experiment and Zeta potential, PAC30 can be effectively adsorbed on the surface of insoluble sediments, and the SEM images show that, after adding PAC30, the particles are tightly packed, and the volume of insoluble sediments is significantly reduced. In the large-scale model experiment, the expansion rate of PAC30 reached 20%, which proves that the shrinkage agent is a potential method to expand the gas storage volume.