The links between high heat producing granites and large-scale W-Sn deposits: insight from numerical modeling

The granites associated with large-scale W and Sn deposits generally have high concentrations of U, Th, and K, including but not limited to the Cornubian Batholith in Southwest England, the Krušné hory/Erzgebirge Batholith in Central Europe, the Sardinian Batholith in Italy, and the Gejiu Batholith and the Qianlishan granitic complex in South China. These granites can be classified as high heat producing (HHP) granites (>5 μW m-3) because of high radiogenic heat production. However, how long radiogenic heat can prolong the suprasolidus lifetime of magmas and whether radiogenic heat exerts an influence on later W and Sn mineralization is poorly understood. To answer these questions, finite element numerical modeling was established to link magma cooling by heat conduction with diffusion of W, Sn, and H2O from silicate melts to coexisting aqueous fluids before the solidus is reached. The magma size (vertical thickness of 4–5 km and horizontal length of 20 km) is constrained by the granites associated with large-scale W and Sn deposits. The modeling results suggest that the suprasolidus lifetimes of HHP magmas are positively correlated with the heat production and magma thickness and negatively correlated with the solidus temperatures and the thermal conductivity of host rocks. Average radiogenic heat of 5–10 μW m-3, together with decreased solidus temperatures due to magmatic differentiation and a moderate thermal conductivity of host rocks, can prolong the suprasolidus lifetime of HHP magmas by 49–427 ka (1 Ma = 1000 ka), corresponding to 11–85 % of the suprasolidus lifetime of equally sized magmas with normal radiogenic heat (2 μW m-3). From the available gravity modeling data, over half of the granites associated with large-scale W and Sn deposits are at least 1 km thicker than the values calculated from the empirical power–law equation, and the modeling results indicate that an increase of 500–1000 m in magma thickness prolongs the suprasolidus lifetimes of HHP magmas (5 μW m-3) by 50–74 %. During magma cooling before solidus is reached, the diffusion of W and Sn is at least several orders of magnitude slower than that of H2O in hydrous melts; thus, the equilibrium partitioning of these two metals between silicate melts and coexisting aqueous fluids is not reached, and the metal diffusion from melts is a rate-limiting step. The prolongation of the suprasolidus lifetimes by radiogenic heat and decreased solidus temperatures can allow extraction of 17–95 % more W and Sn from silicate melts before the solidus is reached and increase the possibility of producing W and Sn mineralization at later stages. Therefore, the coexistence of HHP granites and large-scale W and Sn deposits is not accidental.