The paper proposed an experimental measurement to identify the fluid-induced force and static stiffness coefficients. A three-dimensional fluid model of the labyrinth seals was also established. And the static characteristics under different eccentricities and inlet pressure were studied. Theoretical results show a good agreement with the experiment results. The labyrinth seal with different eccentricity ratios produces a de-centered fluid-induced force and a negative direct static stiffness, which cause the rotor deviating from the geometric center of the stator. Both the fluid-induced force and negative direct static stiffness coefficient with a value of −13.5 kN/m to −72 kN/m increase with increasing eccentricity and inlet pressure. Particularly, the direct static stiffness coefficient shows a relatively significant increase with a high eccentricity ratio (∼>40%). The static instability is mainly due to the fact that the fluid velocity in the small clearance increases more rapidly along the leakage path. The inertial force is increased significantly and the pressure decreases. This results in a greater pressure distribution in the larger clearance. The fluid force and direct static stiffness coefficient that tend to push the rotor away from the stator center are produced, and eventually lead to the static instability of the labyrinth seal.

The permeability of tight shale formations varies from micro-Darcy to nano-Darcy. Recently, hydrogen peroxide (H₂O₂) was tested as an oxidizer to remove the organic matter in the rock in order to increase shale permeability. In this study, shale particles were reacted with hydrogen peroxide solutions under different temperature and pressure conditions in order to “mimic” underground geology conditions. Then, low-temperature nitrogen adsorption and desorption experiments were conducted to measure the pore diameters and porosity of raw and treated shale samples. Moreover, scanning electron microscopy (SEM) images of the samples were analyzed to observe pore structure changes on the surface of shale samples. From the experiments, it was found that the organic matter, including extractable and solid organic matter, could react with H₂O₂ under high temperature and pressure conditions. The original blocked pores and pore throats were reopened after removing organic matter. With the increase of reaction temperature and pressure, the mean pore diameters of the shale samples decreased first and then increased afterwards. However, the volume and Brunauer–Emmett–Teller (BET) surface areas of the shale particles kept increasing with increasing reaction temperature and pressure. In addition to the effect of reaction temperature and pressure, the pore diameter increased significantly with the increasing reaction duration. As a result, H₂O₂ could be used to improve the shale permeability.

In this study, two shale samples with different maturities, from Geniai, Lithuania (R_o = 0.7%), and Wenjiaba, China (R_o = 2.7%), were selected for open-system pyrolysis experiments at 400 °C and 500 °C, respectively. The generation of isotopic gases from the shales with different maturities was investigated, and the effects of pyrite catalysis on the carbon isotopic compositions were also studied. It was found that CO₂, CH₄ and their isotopic gases were the main gaseous products of the pyrolysis of both shales, and more hydrocarbon gases were generated from the low-maturity Geniai shale. The δ13C1 values fluctuated from −40‰ to −38‰, and δ¹³C₂ showed higher values (−38‰~−34‰) for the Geniai shale. In addition, its δ¹³C_CO2 values ranged from −28‰ to −26‰. Compared with the Geniai shale, lower δ¹³C₁ values (−43‰~−42‰) and higher δ¹³C_CO2 values (−19‰~−14‰) were detected for the Wenjiaba shale. As temperature increased, CH₄ became isotopically lighter and C₂H₆ became isotopically heavier, which changes were due to the mass-induced different reaction rates of ¹²C and ¹³C radicals. Furthermore, the pyrite made the kinetic isotope effect stronger and thus made the CH₄ isotopically lighter for both shales, especially at the lower temperature of 400 °C.