Large-scale chemical lateral heterogeneities are inferred in the Earth's lowermost mantle by seismological studies. We explore the model space of thermochemical convection that can maintain reservoirs of dense material for a long period of time, by using similar analysis in 3-D spherical geometry. In this study, we focus on the parameters thought to be important in controlling the stability and structure of primordial dense reservoirs in the lower mantle, including the chemical density contrast

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... between the primordial dense material and the regular mantle material (buoyancy ratio), thermal and chemical viscosity contrasts, volume fraction of primordial dense material and the Clapeyron slope of the phase transition at 660 km depth. We find that most of the findings from the 3-D Cartesian study still apply to 3-D spherical cases after slight modifications. Varying buoyancy ratio leads to different flow patterns, from rapid upwelling to stable layering; and large thermal viscosity contrasts are required to generate long wavelength chemical structures in the lower mantle. Chemical viscosity contrasts in a reasonable range have a second-order role in modifying the stability of the dense anomalies. The volume fraction of the initial primordial dense material does not effect the results with large thermal viscosity contrasts, but has significant effects on calculations with intermediate and small thermal viscosity contrasts. The volume fraction of dense material at which the flow pattern changes from unstable to stable depends on buoyancy ratio and thermal viscosity contrast. An endothermic phase transition at 660 km depth acts as a 'filter' allowing cold slabs to penetrate while blocking most of the dense material from penetrating to the upper mantle.