Numerical experiments of thermochemical mantle convection in 2‐D spherical annulus geometry are performed to investigate the effects of compositional viscosity ratio (ΔηC) on the long‐term evolution of reservoirs of dense, primordial material in the lowermost mantle of the Earth. The internal heating rate in the primordial material is larger than in the ambient mantle by a factor of 10, accounting for the fact that this material may be enriched in radiogenic elements. We find that if the chemical density contrast is large (128 kg/m3), ΔηC plays only a second‐order role on the long‐term stability of these reservoirs. As the chemical density contrast decreases to smaller values (90 kg/m3), ΔηC plays a more significant role. More specifically, when ΔηC is large, around 10 or larger, convection within the reservoirs of primordial material is less vigorous, which increases the temperature and thermal buoyancy of these structures. This, in turn, can eventually lead them to become unstable, with the majority of the primordial material being advected into the large‐scale mantle circulation.