Experimental petrology constraints on the recycling of mafic cumulate: a focus on Cr-spinel from the Rum Eastern Layered Intrusion,Scotland

The ¹⁷⁶Lu–¹⁷⁶Hf and ¹⁴⁷Sm–¹⁴³Nd decay systems are routinely used to determine garnet (Grt)–whole-rock (WR) ages; however, the ¹⁷⁶Lu–¹⁷⁶Hf age of garnet is typically older than the ¹⁴⁷Sm–¹⁴³Nd age determined from the same aliquots. Here we present experimental data for Lu³⁺ and Hf⁴⁺ diffusion in garnet as functions of temperature, pressure and oxygen fugacity and show that the diffusivity of Hf⁴⁺ in almandine/spessartine garnet is significantly slower than that of Lu³⁺. The diffusive closure temperature (T _C) of Hf⁴⁺ is significantly higher than that of Nd³⁺, and although this property is partly responsible for the observed ¹⁷⁶Lu–¹⁷⁶Hf and ¹⁴⁷Sm–¹⁴³Nd Grt–WR age discrepancies, the difference between the T _C-s of Lu³⁺ and Hf⁴⁺ could lead to apparent Grt–WR ¹⁷⁶Lu–¹⁷⁶Hf ages that are skewed from the age of Hf⁴⁺ closure in garnet. In addition, the slow diffusivity of Hf⁴⁺ indicates that the bulk of metamorphic garnets retain a substantial fraction of prograde radiogenic ¹⁷⁶Hf throughout peak metamorphic conditions, a phenomenon that further complicates the interpretation of ¹⁷⁶Lu–¹⁷⁶Hf garnet ages and invalidates the use of analytical T _C expressions. We argue that the diffusion of trivalent rare earth elements in garnet becomes much faster when their concentration level falls below a few hundred ppm, as in the experiments of Tirone et al. (Geochim Cosmochim Acta 69: 2385–2398, 2005), and further argue that this low-concentration mechanism is appropriate for modeling the susceptibility of ¹⁴⁷Sm–¹⁴³Nd garnet ages to diffusive resetting.     

Calcite Dissolution Kinetics

We compare the canonical treatment of calcite’s dissolution rate from the literature in a closed system, particle batch reactor, with the alternative approach suggested by Truesdale (Aquat Geochem, 2015). We show that the decay of rate over time can be understood in terms of the evolution and distribution of reactive sites on the surface of these particles. We also emphasize that interpretation of observed rates must not exclude the fundamental role of crystal defects, whose importance is already implicitly reflected in the common form of rate laws in geochemistry. The empirical behavior of overall rate in closed systems, such as those described by Truesdale, may thus reflect relationships between defect centers and the generation of steps over the calcite surface (previously documented for silicates), such that below a critical free energy limit, there is insufficient driving force to open hollow cores and thus a loss of reaction mechanism. Dissolution in this very-near-equilibrium regime will be dependent on the distribution of extant steps and the energetics of new kink site nucleation. However, these sensitivities are complicated in the case of particle systems by grain boundaries, edges, corners, and other terminations. Such discontinuities constitute a defect class whose overall kinetic importance will be strongly tied to particle diameter and which can act independently of the internal strain field imposed by screw and edge dislocations.     

Efficiency of a two-step upscaling method for permeability evaluation at Darcy and pore scales

This work presents a new subdivision method to upscale absolute permeability fields. This process, called two-step method, consists in (i) solving micro-scale equations on subdomains obtained from the full domain regular decomposition and (ii) solve a second upscaling with Darcy’s law on the permeability fields obtained in the first step. The micro-scale equations used depend on the case studied. The two-step upscaling process is validated on randomly generated Darcy-scale permeability fields by measuring the numerical error induced by upscaling. The method is then applied to real domains obtained from sandstone micro-tomographic images. The method specificities due to pore-space structure are discussed. The main advantage of the two-step upscaling method resides in the drastic reduction of computational costs (CPU time and memory usage) while maintaining a numerical error similar to that of other upscaling procedures. This new upscaling method may improve permeability predictions by the use of finer meshes or larger sample volumes.