Several icy moons and dwarf planets appear to have hosted subsurface liquid water. Liquid water intruding upwards into the icy outer shells of these worlds freezes, forming ice and (from ocean solutes) non-ice solids. Here, we model concentrated aqueous solutions below 273 K to simulate the compositional evolution of freezing spherical intrusions. Starting solutions are based on five previously reported compositional end members for Europa’s ocean. For moderate-pH end members dominated by chloride, sulfate, and/or carbonate, the solids formed include Ca-, Mg-, and Na-sulfates and -carbonates, as well as Na- and K-chlorides. For silica-rich, high-pH end members, abundant amorphous silica forms with, potentially, similarly abundant NaOH and KOH. We further develop a new numerical model to compute the spatial distribution of the formed solids and residual brine as freezing progresses. If non-ice solids settle to the bottom, their deposits tend to have stacked hourglass shapes, widening each time the crystallization temperature of a new solid is reached. We discuss the applicability of this model to vertical fractures and global freezing of a subsurface ocean. These results inform (i) how compositional heterogeneities may affect the thermophysical properties of ice shells, which in turn influence convective and cryovolcanic transport, (ii) the compatibility of brine pockets with physicochemical conditions suitable for microbial life, and (iii) possible measurements of compositional heterogeneities within ice shells by spacecraft such as NASA’s Europa Clipper and ESA’s JUICE missions. The methodology developed here is applicable to other ice-covered ocean worlds.