An atypical strength anisotropy manifesting itself in a monotone decrease in strength with decreasing angle between the maximum compressive stresses and the bedding plane was found in several series of independent tests of Cenomanian sandstone samples on a true triaxial loading facility. In the case of anisotropy of this type, an equal component stress field in the rock mass can cause breakouts on well walls in two opposite directions. Such breakouts were observed in direct physical modeling in samples with holes under the action of equal component compression. In an analysis of logging measurements, such breakouts in wells are usually interpreted as caused by the presence of an unequal component stress field in the rock mass. The presented data indicate the possibility of other interpretations.

When studying the dynamics of a wave solid-state gyroscope, various approximate methods are widely used. This article describes a method for obtaining an exact solution to the equation of oscillations of a thin inextensible ring rotating with an arbitrarily varying angular velocity. The solution obtained can be used to assess the accuracy of approximate methods.

In 1891, Professor George H. Brian demonstrated the effect of standing wave precession in an elastic axisymmetric shell rotating about an axis of symmetry. To explain the effect, Brian turned to a mathematical description of elastic vibrations of a thin circular ring. As a result, he obtained a formula connecting the constant angular velocity of rotation of the ring in its plane with the speed of precession relative to it of a standing wave of elastic vibrations. Later, this formula was used to explain the effect of rotation of a standing wave in a hemispherical resonator when the resonator itself is rotated around its axis of symmetry. At the same time, the angular rate of rotation was no longer assumed to be constant, and Brian’s ratio between speeds was tacitly extended to the ratio between the angles of rotation. In fact, this meant the discovery of the effect of inertness of elastic waves. In the present study, an already complete spherical resonator is considered, and the plane rotation of the resonator is replaced by a spatial one. The generalized Brian effect is also spatial.

Abstract A model has been developed for describing stress state and filtration of rocks that include creep-like effects. The model describes elastic-inelastic transition, and further deformation in inelastic region. The key point consists in accounting for anisotropy of elastic, ultimate and filtration properties. The model is particularized for the properties of rocks of one of oil deposits of Russia.

The aim of this sutdy is to research the time dependence of deformations under complex stress conditions arising in the ground formation during the exploitation of oil and gas fields. The experiments were carried out on the IP Mech triaxial independent loading test system on the rocks of the Prirazlomnoye oil field using loading programs simulating the stress state in the near-borehole region with a decrease in pressure in the well. Experimental dependences of deformations on time during step loading are presented. The basic requirements for constructing a model of a stress-strain state taking into account the influence of time effects are discussed.

An idea of using computer mechanics for inertial navigation systems is given and examples are presented. The equations, algorithms, and properties of the pendulum-type strapdown inertial navigation system are analyzed. As a result, it has been stated that such a system is analogous to analytical systems. A similar comparison for both semi-analytical and strapdown inertial navigation systems, in which the Schuler's pendulum models are described in a horizontal coordinate system, is carried out. An analogy of their properties is established. By comparing the analytical system, platform axes of which are directed along the axes of the inertial coordinate system (orientation of the Schuler's pendulum is also described in the inertial coordinate system), and the strapdown inertial navigation system with the same orientation of the platform's computer model (the comparison is also made for the operation algorithms of such systems), an analogy of such systems has been established. The degree of use of computer mechanics in all types of strapdown inertial navigation systems is much greater than in platform ones. According to the degree of utilization for principles of computer mechanics, types of inertial navigation systems can be arranged in the following order: strapdown pendulum, other strapdown systems, semi-analytical, analytical, and geometric platform inertial navigation systems. Their accuracy depends on the degree of sophistication of the element base, that is, on sensitive elements and on-board computers. We claim that the smaller the volume and mass of the mechanical part of the system the better its weight-and-dimensional characteristics and cost.

The paper presents the results of the investigation of the strain-strength properties of rocks (dolomites) raised from a depth of more than 6 km of the exploration well of the Kainsayskaya Field. The experiments were carried out on a unique experimental setup – the Triaxial Independent Load Test System of IPMech RAS on cubic specimens with an edge of 40 mm. Two triaxial tests were performed on two specimens showing the presence of strong strength anisotropy of the rock. A physical simulation of the pressure reduction process in deep wells near an open borehole and the tip of a perforation hole was performed on three specimens. The conducted studies have revealed a rather low strength of the studied rocks, despite the great depths of their lying under the conditions of high rock pressure. They have shown that the beginning of the rock destruction depends vastly on the type of stress state arising in the formation. Carrying out physical modeling of geomechanical processes in oil and gas reservoirs using true triaxial loading is of great importance from the point of view of justifying methods of influence on deep-lying strata in order to increase the productivity of wells, as well as reduce risks of well destruction during their drilling and operation.

The approach to modeling geomechanical processes in the well vicinity including mathematical modelling of deformation, fracture and filtration as well as experimental determining the parameters involved, under conditions, corresponding to the real in situ ones is presented. The approach involves three stages: (i) choosing the mechanical model and its adopting to the considered problem; (ii) determining the model parameters by using the direct experiments; (iii) mathematical modeling of deformation, fracture and filtration processes in question. The important mechanical model feature is that it accounts for anisotropy of mechanical and filtration properties and dependence of yield transition on volumetric stresses and pore pressure. Another important peculiarity consists in using the experimentally determined dependences of permeability on stress-strain state. The results of the experimental determination of the model parameters for two lithotypes of Kirinsky field and one lithotype of Filanovsky field using the Triaxial Independent Loading Test System (TILTS) are given. Numerical simulation for the used model for the cases of uncased and perforated bottomhole is presented. The stress concentrations and production rate are calculated. The results of the work carried out demonstrate the capability of the approach to solve geomechanical problems in order to optimize technological processes.

The paper proposes a deformation and fracture model for anisotropic stratified rocks and presents theoretical and experimental data on how the rock strength and fracture geometry are influenced by principal stresses and their orientation to bedding planes. Two possible mechanisms are considered for rock fracture under true triaxial load: along bedding planes of weakness and along planes in which Mohr-Coulomb stresses reach a critical combination with cohesion coefficients and internal friction angles typical of the rock. The transition of rocks to inelastic deformation is described in the context of two criteria of which one accounts for the above fracture mechanisms and the other, being a semi-empirical analogue of the Hill yield criterion, accounts for the effect of normal stress. The experimental data presented are for the strain and strength properties of rocks sampled from the Fedorovskoye and Talakanskoye oil and gas fields and tested on an original loading system for true triaxial compression with lateral pressure (similar to the Karman scheme) and for generalized shear (three unequal and nonmonotonic principal stresses). The experimental and theoretical results, including total stress-strain curves, are in good qualitative agreement and demonstrate the possibility to evaluate the parameters entered in the model from tests of particular rocks.

A geomechanical approach to modeling deformation and seepage is presented. Three stages of modeling are described: choice of an appropriate mechanical model and its adaptation to the case in question, experimental determination of parameters of the model, simulation of processes of seepage for particular con figurations of the well. The applied model allows describing the main specific characteristics of mechanical behavior of the collector: the influence of the pore pressure on deformation; the influence of not only shear but also comprehensive stresses and pore pressure on the transition to inelastic behavior; the appearance of inelastic volumetric deformation and its nontrivial dependence on the stress state; the anisotropy of elastic, strength and seepage properties; non-obvious dependence of permeability on the stress strain state. The model unites essential characteristics of Hill's plastic flow theory for anisotropic materials and the Drucker-Prager theory for inelastic deformation of soils. The results of experimental determination of the involved parameters obtained using true triaxial loading system for the collector of Vladimir Filanovsky field in the Caspian Sea are presented.

Most sedimentary rocks have layered structure, and their strength properties are therefore anisotropic; as a consequence, the rock strength depends on the direction of the applied stresses. In this case, various fracture mechanisms are possible. The following two possible fracture mechanisms are considered: actions along the bedding planes, which are weakening surfaces, and along the planes where stresses exceeding the total rock strength are attained. A triaxial independent loading test bench was used to study the fracture conditions for layered rocks composed of productive oil-and-gas strata in complex true triaxial loading tests. The study shows a good qualitative agreement between experimental results and theoretical estimates.

The motions of the complex process of oscillations of the Earth’s pole are separated. On the basis of the precise measurement data of the International Earth’s Rotation Service (since 1962) by means of the least squares technique and spectral analysis, the major components of the motion in the principal approximation are determined. It is established that they are the slow trend and the sum of motions along the circles with annual and Chandler periods. For a difference process, the spectral and integral characteristics are found.

A new approach for the creation of scientific foundations for effective and environmentally safe recovery of methane from coal seams is proposed. A virgin coal seam possesses very low permeability. Free gas is contained in isolated microscopic pores and cracks of the coal seam under a pressure close to the rock pressure. An oriented system of cracks, which forms a coupled system of filtration channels, can be formed by means of directed unloading of the rock pressure from the seam due to expanding gas energy. The parameters of the manufacturing effect on the seam are determined based on physical modeling of actual mechanical and filtration processes using the experimental installation of truly three-axial loading and mathematical modeling.

The motion of a Foucault pendulum is studied in terms of variations in the solid angle. A numerical example is considered.

Some results of the studies performed in the framework of the RAS Presidium Programs “Fundamental basis of new technologies in the oil and gas industry” and “Oil from the deep horizons of sedimentary basins as the main source for replenishment of the raw hydrocarbon resource base; theoretical and applied aspects” that are implemented by RAS researchers in new scientific-methodological and technical solutions seeking promotion in FEC enterprises are presented. Special attention is paid to the problems of oil and gas extraction, such as increase of the oil recovery coefficient, improvement of the contents of information about core samples, and hard-to-extract reserves (highly viscous oil, low permeable reservoirs, shale oil and gas). Theoretical principles of the technology of influence on the oil and gas deposits in anisotropic structures are elaborated. It is shown that the relative phase permeabilities depend not only on the saturation, but also on the direction of displacement. A new method for complex labstudy of the anisotropic samples is revealed to determine the absolute and relative phase permeabilities. Technologies are developed to resolve the problems of reduction of the water and solid phase contents in the well production, increase in the well debit and oil recovery coefficient as a result of the task-oriented choice of operations and parameters of the influence.

We present the experimental results of true triaxial independent loading test bench studies of the influence of a triaxial stress state with unequal components on the filtration properties of rock in oil and gas gathering mains. We show that the permeability of rock subjected to stresses can irreversibly decrease or increase. The discovered effects are of great importance when designing optimal oil and gas well drilling and operation regimes.

The methods of theoretical and celestial mechanics and mathematical statistics have been used to prove that the Earth’s motion relative to the center of mass, the polar wobble, in the principal approximation is a combination of two circumferences with a slow trend in the mean position corresponding to the annual and Chandler components. It has been established that the parameters (amplitude and phase shift) of the annual wobble are stable, while those of the Chandler component are less stable and undergo significant variations over the observed time intervals. It has been proven that the behavior of these polar motion parameters is attributable to the gravitational-tidal mechanisms of their excitation.