This study deals with 2D simulations of curvilinear multi-stage hydro-fracture growth in a reserv... more This study deals with 2D simulations of curvilinear multi-stage hydro-fracture growth in a reservoir. The numerical model employs the method of complex singular integral equations, the SIE method. The crack path is found by applying the criterion of maximum tensile stress at the fracture tip. The study investigates the fracture development for different initial spacings between the fractures, in-situ stresses and the values of fluid pressure that can be different for different cracks.
It is known that during the flow, if the displacing fluid can chemically react with the component... more It is known that during the flow, if the displacing fluid can chemically react with the components of porous medium and with the release of a gas phase, then such a flow regime can be unstable. During this process, pressure fluctuations can be observed, and the displacing fluid will move in “waves”. In the course of our research, a simple mathematical model was proposed that provides a qualitative explanation of the reasons for the emergence of such a phenomenon; laboratory modeling was carried out, and the criterion of the “waves” formation was found, depending on the concentration of chemically active components. The proposed model can predict the emergence of the wave instabilities in a laboratory experiment, which will allow to carry out a future experiment on a larger scale.
A thermodynamically consistent model of a double porosity medium with scattered fracture of a mat... more A thermodynamically consistent model of a double porosity medium with scattered fracture of a matrix is developed. Fracture formation in the matrix is facilitated by the anomalously high reservoir pressure. It is assumed that that damage development in the matrix enhances mass transfer between the subsystems of a double porosity medium. By the example of the problem of productivity of a long cylindrical well, the influence of the abnormal high reservoir pressure on the fluid flow rate is qualitatively demonstrated.
The possibility of excitation of oscillations in a Schumann resonator in the atmosphere of Mars i... more The possibility of excitation of oscillations in a Schumann resonator in the atmosphere of Mars is discussed. On Earth, the main source of energy in the resonator cavity are thunderstorms at tropical latitudes. On Mars, electric phenomena are possible during dust events such as dust columns and dust storms. The charging of dust grains in a dust column on the surface of Mars is considered and the possible values of the electric fields generated by the column are determined. Estimates of the amplitude of oscillations in a Schumann resonator on Mars are obtained and compared with the amplitudes of oscillations in a Schumann resonator on Earth.
В работе обсуждается возможность моделирования анизотропии прочности слоистой упругой среды с исп... more В работе обсуждается возможность моделирования анизотропии прочности слоистой упругой среды с использованием скалярного параметра поврежденности. Сформулированы термодинамически согласованные определяющие уравнения. С помощью пакета SIMULIA/Abaqus моделируется процесс растяжения и сжатия образцов. Результаты расчета с использованием предложенной модели сравниваются с известными из литературы экспериментальными данными и предсказаниями традиционных моделей. Ключевые слова: разрушение, теория поврежденности, анизотропия, термодинамическая согласованность, пользовательские подпрограммы
A model of damage accumulation in a porous medium with a brittle skeleton saturated with a compre... more A model of damage accumulation in a porous medium with a brittle skeleton saturated with a compressible fluid is formulated in the isothermal approximation. The model takes account of the skeleton elastic energy transformation into the surface energy of microcracks. In the case of arbitrary deformations of an anisotropic material, constitutive equations are obtained in a general form that is necessary and sufficient for the objectivity and thermodynamic consistency principles to be satisfied. We also formulate the kinetics equation ensuring that the scattered fracture dissipation is nonnegative for any loading history. For small deviations from the initial state, we propose an elastic potential which permits describing the principal characteristics of the behavior of a saturated porous medium with a brittle skeleton. We study the acoustic properties of the material under study and find their relationship with the strength criterion depending on the accumulated damage and the material current deformation. We consider the problem of scattered fracture of a saturated porous material in a neighborhood of a spherical cavity. We show that the cavity failure occurs if the Hadamard condition is violated.
This study is aimed at application of the method of complex singular integral equation (SIE) to t... more This study is aimed at application of the method of complex singular integral equation (SIE) to the problem of crack propagation in non-uniform stress field. The paper examines one actual problem of oil and gas production: modeling of the hydrofracture trajectories in a reservoir subjected to non-uniform distributions of pore pressure. A modification of the method of mechanical quadratures is used to solve the SIE to simulate the hydro-fracture trajectory. The modification addresses discontinuities in the loads acting on the hydrofracture and provides quite accurate and fast solutions for the stress intensity factors. The crack path is modeled by a polygonal line such that the orientation of every subsequent leg is chosen by the criterion of maximum tensile stresses at the crack tip calculated for the current configuration. Different interposition the hydrofracture and the injection wells are examined.
The paper examines an actual problem of oil and gas production ‐ modelling of the hydro-fracture ... more The paper examines an actual problem of oil and gas production ‐ modelling of the hydro-fracture trajectories depending on non-uniform distributions of pore pressure. The results could serve for improvement of the design of hydraulic fracturing in the oil/gas fields. The methods of the plane elasticity theory and fracture mechanics are employed [6, 8]. It is assumed, that in addition to the uniform field of natural stresses, the reservoir is also subjected to additional stresses caused by technological reasons, which makes the total stress field to be non-uniform. Therefore, the objective of this study is to model a curvilinear crack path in an elastic inhomogeneous-loaded plane depending on the different mechanical parameters that control the stress state of the reservoir. The method of boundary integral equations is used [8] for simulation of the crack trajectory . The algorithms of step-by-step determination of the crack trajectory using the criterion of maximum tensile stresses at the crack end have been developed. For numerical realization we suggest a special modification of the method of mechanical quadratures that is capable to provide effective and fast solutions of the corresponding system of singular integral equations. The solution for the hydro-fracture path have been simulated for several cases of non-uniform stress fields caused by water injection in a well.
This study is aimed at simulation of numerous curvilinear hydro-fracture trajectories in the fram... more This study is aimed at simulation of numerous curvilinear hydro-fracture trajectories in the framework of the mechanics of brittle fracture. The numerical model is based on the method of singular integral equations, SIE. The process of fracture propagation is considered as quasi-static, it is presented by iterations of the stationary step-by-step states, for which the SIE is solved at every step to calculate the stress intensity factors for the current configuration of the fracture system. The trajectory of the fracture is found by applying the criterion of maximum tensile stress at the crack tips and the crack closure is controlled at every step. Two types of fracture growth have been analysed: simultaneous and subsequent for different values of spacing and in-situ stress ratio.
The phenomenological model of microcracks evolution in laminated rocks was developed under an iso... more The phenomenological model of microcracks evolution in laminated rocks was developed under an isothermal approximation. The general form of the constitutive relations of porous media with microcracks was obtained. This form is necessary and sufficient for carrying out the principle of objectivity and the principle of thermodynamic consistency. The approximation of infinitesimal deformations of medium was investigated. The elastic potential of transversal isotropic brittle rocks was constructed. It involves latent energy of damage and terms which characterize elastic energy release due to damage evolution.
Gas-hydrates are perspective sources of hydrocarbons. Fortunately gas-hydrates development is acc... more Gas-hydrates are perspective sources of hydrocarbons. Fortunately gas-hydrates development is accompanied by some difficulties connected with gas-hydrates dissociation. One of them is strength deviation of rock. When gas-hydrates fasten grains of skeleton together elastic solid skeleton can transform to granular or visco-plastic media due to gas-hydrates dissociation. Consequences of these phenomena can be disastrous and can have a form of borehole instability, reservoir consolidation, and dramatic decline of permeability. Adequate model of these phenomena should combine approaches of visco-plastic media mechanics, theory of phase transformation and multiphase flow. In this work gas-hydrates dissociation is described by scalar parameter of dissociation level. The state of constitutive equations of porous medium with gas-hydrates is completed by law governing the evolution of this dissociation parameter. A one-dimensional problem of porous medium consolidation due to gas-hydrates dis...
<p>Complex structure of a skeleton of saturated porous medium can have a gr... more <p>Complex structure of a skeleton of saturated porous medium can have a great influence on the processes of heat and mass transfer.<span> </span></p><p>There are various approaches to the description of<span>  </span>two-phase flow: direct numerical calculation of fluid flow in the pore space, multicontinuous models with the laws of mass exchange between continua, single-continuum models of non-equilibrium flow. In the family of isothermal non-equilibrium filtration models, the relative phase permeabilities and capillary pressure are functions not of current saturation but of their change history.</p><p>In this work we generalize the relaxation model of capillary nonequilibrium to the non-isothermal case. We introduce two internal thermodynamic parameters (capillary and thermal nonequilibrium) which depend on change history of saturation and temperature. In the model relative phase permeabilities and capillary pressure are functions of saturation, temperature, and current values of these internal parameters. Based on the analysis of the dissipation inequality, thermodynamically consistent kinetic equations for the evolution of these parameters are proposed. The parameters of the single-continuum model are clarified with double-porosity model of porous media with special structure. Structure of the penetration front of fluid hot (or cold) compared to the skeleton was investigated.</p><p>This work was supported by the Russian Foundation for Basic Research: grant N19-01-00592.<span> </span></p><p> </p>
This study deals with 2D simulations of curvilinear multi-stage hydro-fracture growth in a reserv... more This study deals with 2D simulations of curvilinear multi-stage hydro-fracture growth in a reservoir. The numerical model employs the method of complex singular integral equations, the SIE method. The crack path is found by applying the criterion of maximum tensile stress at the fracture tip. The study investigates the fracture development for different initial spacings between the fractures, in-situ stresses and the values of fluid pressure that can be different for different cracks.
It is known that during the flow, if the displacing fluid can chemically react with the component... more It is known that during the flow, if the displacing fluid can chemically react with the components of porous medium and with the release of a gas phase, then such a flow regime can be unstable. During this process, pressure fluctuations can be observed, and the displacing fluid will move in “waves”. In the course of our research, a simple mathematical model was proposed that provides a qualitative explanation of the reasons for the emergence of such a phenomenon; laboratory modeling was carried out, and the criterion of the “waves” formation was found, depending on the concentration of chemically active components. The proposed model can predict the emergence of the wave instabilities in a laboratory experiment, which will allow to carry out a future experiment on a larger scale.
A thermodynamically consistent model of a double porosity medium with scattered fracture of a mat... more A thermodynamically consistent model of a double porosity medium with scattered fracture of a matrix is developed. Fracture formation in the matrix is facilitated by the anomalously high reservoir pressure. It is assumed that that damage development in the matrix enhances mass transfer between the subsystems of a double porosity medium. By the example of the problem of productivity of a long cylindrical well, the influence of the abnormal high reservoir pressure on the fluid flow rate is qualitatively demonstrated.
The possibility of excitation of oscillations in a Schumann resonator in the atmosphere of Mars i... more The possibility of excitation of oscillations in a Schumann resonator in the atmosphere of Mars is discussed. On Earth, the main source of energy in the resonator cavity are thunderstorms at tropical latitudes. On Mars, electric phenomena are possible during dust events such as dust columns and dust storms. The charging of dust grains in a dust column on the surface of Mars is considered and the possible values of the electric fields generated by the column are determined. Estimates of the amplitude of oscillations in a Schumann resonator on Mars are obtained and compared with the amplitudes of oscillations in a Schumann resonator on Earth.
В работе обсуждается возможность моделирования анизотропии прочности слоистой упругой среды с исп... more В работе обсуждается возможность моделирования анизотропии прочности слоистой упругой среды с использованием скалярного параметра поврежденности. Сформулированы термодинамически согласованные определяющие уравнения. С помощью пакета SIMULIA/Abaqus моделируется процесс растяжения и сжатия образцов. Результаты расчета с использованием предложенной модели сравниваются с известными из литературы экспериментальными данными и предсказаниями традиционных моделей. Ключевые слова: разрушение, теория поврежденности, анизотропия, термодинамическая согласованность, пользовательские подпрограммы
A model of damage accumulation in a porous medium with a brittle skeleton saturated with a compre... more A model of damage accumulation in a porous medium with a brittle skeleton saturated with a compressible fluid is formulated in the isothermal approximation. The model takes account of the skeleton elastic energy transformation into the surface energy of microcracks. In the case of arbitrary deformations of an anisotropic material, constitutive equations are obtained in a general form that is necessary and sufficient for the objectivity and thermodynamic consistency principles to be satisfied. We also formulate the kinetics equation ensuring that the scattered fracture dissipation is nonnegative for any loading history. For small deviations from the initial state, we propose an elastic potential which permits describing the principal characteristics of the behavior of a saturated porous medium with a brittle skeleton. We study the acoustic properties of the material under study and find their relationship with the strength criterion depending on the accumulated damage and the material current deformation. We consider the problem of scattered fracture of a saturated porous material in a neighborhood of a spherical cavity. We show that the cavity failure occurs if the Hadamard condition is violated.
This study is aimed at application of the method of complex singular integral equation (SIE) to t... more This study is aimed at application of the method of complex singular integral equation (SIE) to the problem of crack propagation in non-uniform stress field. The paper examines one actual problem of oil and gas production: modeling of the hydrofracture trajectories in a reservoir subjected to non-uniform distributions of pore pressure. A modification of the method of mechanical quadratures is used to solve the SIE to simulate the hydro-fracture trajectory. The modification addresses discontinuities in the loads acting on the hydrofracture and provides quite accurate and fast solutions for the stress intensity factors. The crack path is modeled by a polygonal line such that the orientation of every subsequent leg is chosen by the criterion of maximum tensile stresses at the crack tip calculated for the current configuration. Different interposition the hydrofracture and the injection wells are examined.
The paper examines an actual problem of oil and gas production ‐ modelling of the hydro-fracture ... more The paper examines an actual problem of oil and gas production ‐ modelling of the hydro-fracture trajectories depending on non-uniform distributions of pore pressure. The results could serve for improvement of the design of hydraulic fracturing in the oil/gas fields. The methods of the plane elasticity theory and fracture mechanics are employed [6, 8]. It is assumed, that in addition to the uniform field of natural stresses, the reservoir is also subjected to additional stresses caused by technological reasons, which makes the total stress field to be non-uniform. Therefore, the objective of this study is to model a curvilinear crack path in an elastic inhomogeneous-loaded plane depending on the different mechanical parameters that control the stress state of the reservoir. The method of boundary integral equations is used [8] for simulation of the crack trajectory . The algorithms of step-by-step determination of the crack trajectory using the criterion of maximum tensile stresses at the crack end have been developed. For numerical realization we suggest a special modification of the method of mechanical quadratures that is capable to provide effective and fast solutions of the corresponding system of singular integral equations. The solution for the hydro-fracture path have been simulated for several cases of non-uniform stress fields caused by water injection in a well.
This study is aimed at simulation of numerous curvilinear hydro-fracture trajectories in the fram... more This study is aimed at simulation of numerous curvilinear hydro-fracture trajectories in the framework of the mechanics of brittle fracture. The numerical model is based on the method of singular integral equations, SIE. The process of fracture propagation is considered as quasi-static, it is presented by iterations of the stationary step-by-step states, for which the SIE is solved at every step to calculate the stress intensity factors for the current configuration of the fracture system. The trajectory of the fracture is found by applying the criterion of maximum tensile stress at the crack tips and the crack closure is controlled at every step. Two types of fracture growth have been analysed: simultaneous and subsequent for different values of spacing and in-situ stress ratio.
The phenomenological model of microcracks evolution in laminated rocks was developed under an iso... more The phenomenological model of microcracks evolution in laminated rocks was developed under an isothermal approximation. The general form of the constitutive relations of porous media with microcracks was obtained. This form is necessary and sufficient for carrying out the principle of objectivity and the principle of thermodynamic consistency. The approximation of infinitesimal deformations of medium was investigated. The elastic potential of transversal isotropic brittle rocks was constructed. It involves latent energy of damage and terms which characterize elastic energy release due to damage evolution.
Gas-hydrates are perspective sources of hydrocarbons. Fortunately gas-hydrates development is acc... more Gas-hydrates are perspective sources of hydrocarbons. Fortunately gas-hydrates development is accompanied by some difficulties connected with gas-hydrates dissociation. One of them is strength deviation of rock. When gas-hydrates fasten grains of skeleton together elastic solid skeleton can transform to granular or visco-plastic media due to gas-hydrates dissociation. Consequences of these phenomena can be disastrous and can have a form of borehole instability, reservoir consolidation, and dramatic decline of permeability. Adequate model of these phenomena should combine approaches of visco-plastic media mechanics, theory of phase transformation and multiphase flow. In this work gas-hydrates dissociation is described by scalar parameter of dissociation level. The state of constitutive equations of porous medium with gas-hydrates is completed by law governing the evolution of this dissociation parameter. A one-dimensional problem of porous medium consolidation due to gas-hydrates dis...
<p>Complex structure of a skeleton of saturated porous medium can have a gr... more <p>Complex structure of a skeleton of saturated porous medium can have a great influence on the processes of heat and mass transfer.<span> </span></p><p>There are various approaches to the description of<span>  </span>two-phase flow: direct numerical calculation of fluid flow in the pore space, multicontinuous models with the laws of mass exchange between continua, single-continuum models of non-equilibrium flow. In the family of isothermal non-equilibrium filtration models, the relative phase permeabilities and capillary pressure are functions not of current saturation but of their change history.</p><p>In this work we generalize the relaxation model of capillary nonequilibrium to the non-isothermal case. We introduce two internal thermodynamic parameters (capillary and thermal nonequilibrium) which depend on change history of saturation and temperature. In the model relative phase permeabilities and capillary pressure are functions of saturation, temperature, and current values of these internal parameters. Based on the analysis of the dissipation inequality, thermodynamically consistent kinetic equations for the evolution of these parameters are proposed. The parameters of the single-continuum model are clarified with double-porosity model of porous media with special structure. Structure of the penetration front of fluid hot (or cold) compared to the skeleton was investigated.</p><p>This work was supported by the Russian Foundation for Basic Research: grant N19-01-00592.<span> </span></p><p> </p>
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Papers by O. Izvekov