To size any dissolution unit, you need to decide how much salt must be dissolved and the rate of dissolution.  The rate will be determined by the temperature, solubility, particle size, etc.  Much of the determination can be made in the laboratory, with a small quantity of the actual salt and an appropriate quantity of water, at the correct temperature.  The mixing intensity will have a relatively small effect on the rate of dissolution, so long as all of the solids are off the bottom, but not necessarily suspended uniformly.

Once you know the quantity and rate of dissolution, the volume necessary for the vessel can be established.  The tank height should be about the same as the tank diameter, based on the required volume.  The particle size and density difference from the brine will establish the settling characteristics.  Correlations are available for off-bottom suspension with the particle size and density difference.