Electrical resistivity is one of the fundamental physical properties of rocks, and its relationship with fluid saturation is widely used in reservoir evaluation. The interpretation of electrical logs usually relies on the results of rock resistivity tests of cores in the laboratory. In the laboratory, core samples are commonly cut into cylinders, and the resistivity is measured along the axial direction. To determine the rock resistivity along different directions, samples are cut into cubes and tested along three perpendicular directions to obtain resistivity data. The expensive and complicated preparation process of cubic samples and the custom holder requirements limit the use of these tests. We analyzed the advantages and disadvantages of rock resistivity measurements of cylindrical and cubic samples. To overcome the difficulties above, we developed a core holder for radial resistivity measurements and proposed a radial resistivity measurement method for cylindrical samples. Based on the conformal transformation of the complex variable function theory, we established a mathematical model of radial resistivity. We developed a measurement method of radial resistivity according to the mathematical model and verified this approach with isotropic cores. The theoretical calculation results agree with the experimental results. With the radial resistivity measurement method, we effectively tested the resistivity anisotropy of shale. This method has more advantages than existing methods in terms of the sample preparation and realization of various displacement levels and angles. Hence, the proposed method can be widely used.
Rock resistivity is a major geophysical technical parameter in geological and geotechnical engineering, geothermal prospecting, and oil and gas exploration. Its accurate measurement is of great significance to achieve the goal of “carbon peak and carbon neutrality”. To solve anisotropic problems, a method to test the radial resistivity in cylindrical core samples has been proposed and has been deemed the universal method, as it has the virtues of no specially processed sample being needed and nondestructive testing. However, there is still a difference in the radial resistivities obtained from this method and another testing method that is commonly used for cuboid samples. Furthermore, the differences between these methods have not yet been made clear in China or elsewhere. Therefore, we compared the results of the above-two testing methods via numerical simulations after establishing the potential field distribution, and, in combination with their methodological principles, illustrated the differences between the resistivities determined in samples with distinct shapes obtained using the two testing methods, summarized the conditions when there was zero difference and considerable difference when using the two methods, and provided a theoretical basis for the reasonable selection of an appropriate method to test the resistivity anisotropy.
In the oil and gas industry, traditional logging mostly deems that oil and gas reservoirs are characterized by high resistivity, whereas the water layer is often by low resistivity. However, a lot of exploration and development practices on shale gas reservoirs in Sichuan Basin, China, prove that it is hard to characterize a functional relation between resistivity and water saturation using the Archie equation. Therefore, to make clear the mechanism to form low resistivity in shale gas reservoirs, the matrix resistivity was calculated through the percolation network simulation based on pore structure characteristics and mineral compositional parameters. Moreover, the resistivity in low-resistivity laminations of shale was measured through the finite element simulation. In addition, the reasons for such low resistivity in shale were analyzed according to the resistivity-forming mechanism, and the effects of penetration degree, width, quantity, and spatial distribution of the laminations on the resistivity were worked out. Those may provide theoretical support for explaining the phenomenon of low-resistivity gas reservoirs.
In tight gas reservoirs, the major flow channels are composed of micro/nanopores in which the rarefaction effect is prominent and the traditional Darcy law is not appropriate for gas flow. By combining the Maxwell first-order slip boundary condition and Navier–Stokes equations, a three-dimensional (3D) analysis of compressible gas slip flow in a microtube was presented, and the flux rate and pressure variation in the flow direction were discussed. Subsequently, by superimposing the Knudsen diffusion, a gas flux formula applicable to a larger Knudsen number was further proposed and satisfactorily verified by two groups of published experimental data in microtubes or microchannels in the membrane. The results indicate that slip flow and Knudsen diffusion make an important contribution to the total gas flow in the microtube, and their weight increases with an increase in the Knudsen number. By substituting the gas flux formula into Darcy’s law for compressible gas, a new apparent permeability model for tight gas reservoirs was proposed, in which the slippage effect and Knudsen diffusion were synthetically considered. The results indicate that the apparent permeability of tight reservoirs strongly depends on the reservoir pressure and pore-throat radius, and an underestimation value may be predicted by the previously published models. This study provides a case study for evaluating these apparent permeability models, which remains a challenging task in the laboratory.
Anisotropy is a prevailing
property in most substances in the real
world. The thermal conductivity characteristic of anisotropy must
be determined for utilizing geothermal resources and assessing battery
performances. Most core samples were primarily obtained by drilling
and intended to be cylindrical in shape, with the cores resembling
quantities of familiar batteries. Although Fourier’s law could
be used to measure the axial thermal conductivity of square or cylindrical
samples, there is still a need to develop a new method to measure
the radial thermal conductivity of cylindrical samples and evaluate
their anisotropy. Thus, we established a testing method for cylindrical
samples using the theory of complex variable functions following the
heat conduction equation and implemented a numerical simulation to
determine the difference between this method and typical ones via
a finite element model for various samples. Results show that the
method could perfectly gauge the radial thermal conductivity of cylindrical
samples with more powerful availability.
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