Modelos de condutividade térmica em rochas silicáticas, com ênfase em rochas da província Borborema, NE do Brasil

A practical approach to estimate rock thermal conductivities is to use rock models based just on the observed or expected rock mineral content. In this study, we evaluate the performances of the Krischer and Esdorn (KE), Hashin and Shtrikman (HS), classic Maxwell (CM), Maxwell-Wiener (MW), and geometric mean (GM) models in reproducing the measures of thermal conductivity of crystalline rocks.We used 1,105 samples of igneous and metamorphic rocks collected in outcroppings of the Borborema Province, Northeastern Brazil. Both thermal conductivity and petrographic modal analysis (percent volumes of quartz, K-feldspar, plagioclase, and sum of mafic minerals) were done. We divided the rocks into two groups: (a) igneous and ortho-derived (or meta-igneous) rocks and (b) metasedimentary rocks. The group of igneous and ortho-derived rocks (939 samples) covers most the lithologies de_ned in the Streckeisen diagram, with higher concentrations in the fields of granite, granodiorite, and tonalite. In the group of metasedimentary rocks (166 samples), it were sampled representative lithologies, usually of low to medium metamorphic grade. We treat the problem of reproducing the measured values of rock conductivity as an inverse problem where, besides the conductivity measurements, the volume fractions of the constituent minerals are known and the effective conductivities of the constituent minerals and model parameters are unknown. The key idea was to identify the model (and its associated estimates of effective mineral conductivities and parameters) that better reproduces the measures of rock conductivity. We evaluate the model performances by the quantity  that is equal to the percentage of number of rock samples which estimated conductivities honor the measured conductivities within the tolerance of 15%. In general, for all models, the performances were quite inferior for the metasedimentary rocks (34% <  < 65%) as compared with the igneous and ortho-derived rocks (51% <  < 70%). For igneous and ortho-derived rocks, all model performances were very similar ( = 70%), except the GM-model that presented a poor performance (51% <  < 65%); the KE and HS-models ( = 70%) were slightly superior than the CM and MW-models ( = 67%). The quartz content is the dominant factor in explaining the rock conductivity for igneous and ortho-derived rocks; in particular, using the MW-model the solution is in practice vi UFRN/CCET– Dissertação de mestrado the series association of the quartz content. On the other hand, for metasedimentary rocks, model performances were different and the performance of the KEmodel ( = 65%) was quite superior than the HS ( = 53%), CM (34% <  < 42%), MW ( = 40%), and GM (35% <  < 42%). The estimated effective mineral conductivities are stable for perturbations both in the rock conductivity measures and in the quartz volume fraction. The fact that the metasedimentary rocks are richer in platy-minerals explains partially the poor model performances, because both the high thermal anisotropy of biotite (one of the most common platy-mineral) and the difficulty in obtaining polished surfaces for measurement coupling when platyminerals are present. Independently of the rock type, both very low and very high values of rock conductivities are hardly explained by rock models based just on rock mineral content.