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International audience; Methane diffusion in micro- and mesopores of carbonaceous materials is dominated by molecular interactions with the pore walls. As a consequence, the fluid molecules are mainly in a diffusive regime and the laws of fluid mechanics are not directly applicable. A method called the “free volume theory” has been successfully used by different authors to study the diffusion of n-alkanes into microporous carbons. However, we show in this paper that such a method fails to describe the dynamical properties of methane in porous hosts presenting both micro- and mesopores. We further evidence that this theory is limited to structures whose pore diameters are lower than ∼3 nm. We then propose a simple scaling method based on the micro- and mesoporous volume fraction in order to predict diffusion coefficients. This method only requires the knowledge of (i) the host microporous volume fraction and (ii) the self-diffusion coefficient in micropores smaller than 3 nm, which can be obtained using the “free volume theory”, quasi-elastic neutron scattering experiments, or atomistic simulations.

Nuclear Magnetic Resonance (NMR) relaxometry measurements are commonly used to characterize the storage and transport properties of water-saturated rocks. These assessments are based on the proportionality of NMR signal amplitude and relaxation time to porosity (water content) and pore size, respectively. The relationship between pore size and NMR relaxation time depends on pore shape, which is usually assumed to be spherical or cylindrical. However, the NMR response at partial water saturation for natural sediments and rocks differs strongly from the response calculated for spherical or cylindrical pores, because these pore shapes cannot account for water menisci remaining in the corners of de-saturated angular pores. Therefore, we consider a bundle of pores with triangular cross-sections. We introduce analytical solutions of the NMR equations at partial saturation of these pores, which account for water menisci of de-saturated pores. After developing equations that describe the water distribution inside the pores, we calculate the NMR response at partial saturation for imbibition and drainage based on the deduced water distributions. For this pore model, NMR amplitude and NMR relaxation time at partial water saturation strongly depend on pore shape even so the NMR relaxation time at full saturation only depends on the surface to volume ratio of the pore. The pore-shape-dependence at partial saturation arises from the pore shape and capillary pressure dependent water distribution in pores with triangular cross-sections. Moreover, we show the qualitative agreement of the saturation dependent relaxation time distributions of our model with those observed for rocks and soils.

We present a comprehensive statistical analysis of petrophysical properties of rocks of the northeastern Rhenish Massif and the Lower Rhine Embayment in Germany. Properties measured comprise thermal conductivity, specific heat capacity density, porosity, hydraulic permeability, and compressional wave velocity. This robust and statistically reliable data is generally useful for numerical modeling of heat transport processes and helps, in particular, reducing the risk of failure in projects of geothermal energy use. We measured the thermophysical properties of rocks from two geological settings: (1) predominantly little consolidated Tertiary rocks forming the young sedimentary cover of the Lower Rhine Embayment in the condition they arrived in the laboratory; (2) well consolidated Paleozoic rocks from the northeastern Rhenish Massif in both dry and saturated condition. We tested a total of 476 samples from different lithologies in both settings in a comprehensive laboratory program consisting of mineralogical analyses and various petro- and thermophysical measurements at ambient and elevated p-T-conditions. This yields relations between composition and thermophysical properties of different sedimentary rock types and allows distinguishing between effects due to rock matrix and structure. The results are used to prove petrophysical rock models and allow predicting thermal properties of distinct rock types for greater depth. The results show that the thermophysical properties of Paleozoic rocks are mainly controlled by their mineralogical compositions, while thermophysical characteristics of Tertiary rocks are the result of a superposition of properties of their mineral content and the water-filled pore volume.

[1] Studying heat transfer processes in sedimentary crustal rocks requires the correct thermal conductivity of the respective rock type. Often a single value is used for a given rock type, obtained from the measurements on homogenous samples. We demonstrate how variations in rock layering and microfractures on the subcentimeter scale may influence thermal conductivity values at much larger scale. We obtain thermal conductivity images from lab measurements on two different, heterogeneous samples performed with an optical thermal conductivity scanner in two directions. We study different spatial averaging methods for parameterizing the structural heterogeneities and the associated variation of thermal conductivity within the samples. For each of these structural simplifications, we set up a numerical model for a numerical heat transfer experiment in order to determine effective thermal conductivity values in two directions. We compare these values and the mean thermal conductivities obtained from different mixing laws and find that, in heterogeneous rocks, effective and mean thermal conductivity may differ substantially. This may cause significant errors in reservoir-scale simulations of heat transfer with associated severe consequences for estimated heat flow and temperatures.

International audience; The present-day thermal regime of the Arabian plate is affected by the dynamics of the Afar plume and the rifting of the Red Sea and the Gulf of Aden. The Arabian plate is a Precambrian Shield and its thermal regime, before the plume and rifting activities, should be similar to that of other Precambrian Shields with a thick lithosphere. This is consistent with low heat-flow values measured in Saudi Arabia (35–44 mWm− 2), but not with recent measurements in Jordan that show higher heat flow (56–66 mWm− 2). We have conducted measurements in the eastern Arabian plate to obtain 10 new heat-flux values. We also derived 20 heat-flux values from oil exploration wells. Our measurements show that surface heat flux is uniformly low (45 mWm− 2) in the eastern Arabian Shield and is consistent with low crustal heat production (0.7 μWm− 3). A steady-state geotherm for the Arabian platform that intersects the isentropic temperature profile at a depth of 150 km is consistent with the seismic observations. Differences in heat flow between the eastern (60 mWm− 2) and the western (45 mWm− 2) parts of Arabia reflect differences in crustal heat production as well as a higher mantle heat flux in the west. Seismic tomography studies of the mantle beneath Arabia show this east–west contrast. The lithospheric thickness for the Arabian plate is 150 km, and the progressive thinning near the Red Sea is caused by the thermal erosion of the plume. The Afar plume mostly affects the base of the Arabian lithosphere along the Red Sea and the western part of the Gulf of Aden by channeling magmas from the asthenosphere through the rift. The continental domain is not affected by rifting in the Gulf of Aden. The main thermal effect of the Arabian plate is probably the channeling of the Afar plume to the North.

[1] In this paper, we present a method that allows one to correct thermal conductivity measurements for the effect of water loss when extrapolating laboratory data to in situ conditions. The water loss in shales and unconsolidated rocks is a serious problem that can introduce errors in the characterization of reservoirs. For this study, we measure the thermal conductivity of four sandstones with and without clay minerals according to different water saturation levels using an optical scanner. Thermal conductivity does not decrease linearly with water saturation. At high saturation and very low saturation, thermal conductivity decreases more quickly because of spontaneous liquid displacement and capillarity effects. Apart from these two effects, thermal conductivity decreases quasi-linearly. We also notice that the samples containing clay minerals are not completely drained, and thermal conductivity reaches a minimum value. In order to fit the variation of thermal conductivity with the water saturation as a whole, we used modified models commonly presented in thermal conductivity studies: harmonic and arithmetic mean and geometric models. These models take into account different types of porosity, especially those attributable to the abundance of clay, using measurements obtained from nuclear magnetic resonance (NMR). For argillaceous sandstones, a modified arithmetic-harmonic model fits the data best. For clean quartz sandstones under low water saturation, the closest fit to the data is obtained with the modified arithmetic-harmonic model, while for high water saturation, a modified geometric mean model proves to be the best.