You could store the salt. You go up far beyond saturation. Salt sediments on the floor (which also might seal it). When you need brine you pump in seawater into

You could store the salt. You go up far beyond saturation. Salt sediments on the floor (which also might seal it). When you need brine you pump in seawater into a tunnelsystem in the sediment. The saturated brine should be lighter and further up. Overflow to second basin, where it's pumped into the cavern. Thus size comes down to whatever size is needed to store enough salt and or, be big enough to guarantee a certain rate of volume of fully saturated water per time; so basically dimensions that guarantee a phase separation and high enough diffusion rate. And some bad ass pumps (or have the basin be below sealevel and a dam with gates; probably the pumps for reasons of security>efficency in that case)