Continuous Medium Model Research Articles

Research Progress of Three-dimensional Geological Modeling and Multi-field Coupling of Fractured Oil and Gas Reservoirs

Fractured oil and gas reservoirs play an important role in oil and gas exploration and development due to their complex fracture network structure. As the main fluid channel in the reservoir, fractures have a significant impact on the migration, accumulation and exploitation efficiency of oil and gas. This paper summarizes the key geological characteristics of fractured reservoirs, including fracture types, distribution rules and main controlling factors of fracture development, and discusses the influence of fractures on reservoir physical properties. Furthermore, the deterministic and stochastic modeling methods of three-dimensional geological modeling of fractured reservoirs and the latest progress of discrete fracture network modeling technology are introduced in detail. In addition, this paper also discusses in detail the application of multi-field coupling model in the numerical simulation of fluid flow in fractured reservoirs, including continuous medium model and discrete medium model, and their advantages and disadvantages in simulating fluid flow in fractured reservoirs. Finally, this paper summarizes the research progress of multi-physics coupling model of fractured reservoirs, and points out the direction and challenges of future research. Through these studies, it can provide theoretical support and technical guidance for oil and gas exploration and development, in order to achieve more effective development and management of fractured reservoirs.

Lateral kinematic properties of offshore pipe piles embedded in saturated soil considering soil plug effect

AbstractThis study establishes a theoretical framework for analyzing the lateral oscillation of marine pipe piles. The additional mass model is introduced herein to consider the inertial fluctuation effect of the soil plug. Analytical mathematical methods are used to determine the complex impedance variation of the pile over a range of frequency effects. An investigation is performed to determine how the presence of soil plugs changes the lateral complex stiffness and natural frequency of pipe piles. Additionally, comparisons of the applicability of the plane strain model and continuous medium model have been conducted to enable the easy use of the theoretical model. The main conclusions can be drawn as (1) if the fluctuation inertia effect of the soil plug is not taken into consideration, the dynamic active length and the dynamic stiffness of the pipe pile will be underestimated; (2) for the soft soil, the plane strain model may give rise to substantial calculation errors attributed to them regardless of the vertical continuity of the soil, nevertheless, the calculation error decreases rapidly with the increase of soil shear modulus and vibration frequency.

Pore-Scale Numerical Simulation of Acid-Rock Reaction Processes in Carbonate Reservoirs.

In the process of acidizing carbonate reservoirs, dissolution is employed for reservoir modification to enhance recovery rates. This study establishes a numerical model at the pore scale for acid-rock reaction flow based on a microscopic continuum medium model, integrating phase-field theory and component transport models. Subsequently, the results of the Darcy-Brinkman-Stokes model are compared to those of the arbitrary Lagrange-Euler method to validate the accuracy of the model. Finally, the flow behavior of the acid solution at the pore scale and the complex dissolution mechanisms in carbonate reservoirs are analyzed. The research indicates that the microscopic pore-scale dissolution in carbonate reservoirs mainly manifests as five dissolution modes: uniform dissolution, compact dissolution, conical wormholes, dominant wormhole, and ramified wormholes. Different distributions of microfractures will alter the flow state of the acid solution and the rock-acid reaction process within the pores. Once the wormhole breakthrough occurs, there is an increased probability of acid flow through the wormhole to the outlet, leading to a decrease in the effectiveness of the acidizing carbonate reservoirs. A proper understanding of pore-scale acid-rock reaction laws is of great significance for the development of carbonate oil and gas reservoirs.

Effect of fluid patch clustering on the P-wave velocity-saturation relation: a critical saturation model

Quantitative analysis of the relationship between seismic wave velocities and fluid saturation in porous media is of great significance for any fluid injection and extraction operation in subsurface rock formations. However, seismic velocities are not only dependent on the amount of saturation, but also on the distribution of fluid patches and their size. The patch size variation during changes in saturation is oftentimes ignored in modeling studies, even though it is natural to assume that with increasing saturation, fluid patches will form larger and, at some critical saturation, percolating clusters. To capture the evolution of patch size with saturation implied in the velocity-saturation relations, we are inspired by percolation theory. By incorporating the connectivity of water-filled patches in the continuous random medium model, we develop a critical saturation model. We apply this critical saturation model to examine recently reported experimental measurements, specifically analyzing the patch size changes. For measurements of drainage or imbibition processes in four sandstone samples, we indeed find a clear indication of growing patch size with water saturation. The predictions of the critical saturation model are in reasonable agreement with observations. Our approach improves the accuracy of the interpretation of the velocity-saturation relations in partially saturated rocks and forms a basis for exploring its underlying mechanisms.

Об одной новой схеме применения метода конечных элементов в горных науках

At the moment a large number of research papers are being published in the field of mining sciences, utilizing FEM (finite element method) in one way or another. The vast majority of these papers are devoted to solving various engineering problems in mining using different software products such as ABAQUS, PLAXIS, etc. It has been determined that almost all existing works in this field follow the typical scheme for the application of FEM. Materials and methods. The analysis showed that the typical scheme for the application of FEM in mining sciences contains a fundamental error related to the inadequate consideration of the representative volume of rocks during the construction of a continuous medium model and the formation of a discrete model. This leads to a significant degree of inaccuracy in the modeling results. Results and discussion. To resolve the fundamental error, a new scheme for the application of FEM in mining sciences is proposed. It differs from the typical scheme by introducing a new intermediate model between the rock mass and the continuum model. This model, named ‘rock mass body’, represents a set of geoparticles. The sizes of the geoparticles are determined according to the representative volume of the structural or textural components of the rock mass. Comparative analysis has shown that, unlike the typical scheme for the application of FEM, the use of the proposed scheme allows to get solutions with a high degree of accuracy when researching rocks with coarse-grained and medium-grained structures. Conclusion. An analysis of the typical scheme for the application of FEM identified a fundamental error in its use for rock mass modeling tasks. A new scheme has been proposed to correct this error. Suggestions for practical application and direction of future research. The research results can be used to improve the accuracy of finite element models of rock masses. Further research should focus on improving methods for determining the shape of finite elements in relation to the symmetry of the structural and textural components of the rock mass. At the same time, it is necessary to take into account the fracturing of rocks.

A particle-level discrete element model for simulating the performance of MRFs

The particle dynamics model of MRFs (MRFs) is based on the discrete element technique, which takes into account essential MRF variables such as magnetic field, particle parameters, particle volume fraction, carrier fluid properties, and other parameters. Firstly, to digitally characterize the microstructure of MRFs, the particle coordination number, as a new perspective is creatively proposed. The validity and predictability of the created model are then tested in conjunction with the rheological performance studies by comparing it to the known continuous medium model. Finally, based on the proposed model, the influence of each influencing factor on the magnetorheological effect is simulated and regularity analysis is given from the perspective of particles. Linking macroscopic qualities and MRF microstructure, which offers a theoretical basis for the preparation of MRFs with improved performance and prediction of performance under various working situations.

A temporary soil dump settlement and landslide risk analysis using the improved small baseline subset-InSAR and continuous medium model

Abandoned soil disposal in China has become increasingly challenging, which may pose significant safety hazards such as soil settlement and landslides. Interferometry Synthetic Aperture Radar (InSAR) is effective in surface deformation monitoring and Small Baseline Subset-InSAR (SBAS-InSAR) can obtain sufficient coherent point density from the bare soil surface. This study investigated Chishi soil dump in the Shenzhen-Shanwei Special Cooperation Zone (SSSCZ), and a total of 91 Sentinel-1 images from 2019 to 2022 was processed. Accordingly, an improved SBAS-InSAR method was utilized to analyze the soil dump’s time-series deformation, and multi-source remote sensing data were used for auxiliary interpretation. Our results indicate that precipitation, high temperature, and construction vibrations may cause instability of the soil dump. Therefore, a depth-integrated continuous medium model was introduced to analyze the potential landslide risk of the soil dump, which demonstrate that a landslide will likely occur, harm personnel, and damage the buildings surrounding the Chishi soil dump when it was saturated (λ ≥ 0.50). This research can provide a vital case reference for the analysis, interpretation, disaster prevention, and control evaluation of similar soil dumps.

Refined Schemes for Computing the Dynamics of Elastoviscoplastic Media

For a stable numerical solution of the system of equations governing an elastoviscoplastic continuous medium model, a second-order explicit-implicit scheme is proposed. An explicit approximation is used for the equations of motion, and an implicit approximation, for the constitutive relations containing a small relaxation time parameter in the denominator of the nonlinear free terms. A second-order implicit approximation for isotropic and anisotropic elastoviscoplastic models is constructed to match the orders of approximation of the explicit elastic and implicit adjustment steps. Refined formulas for correcting the stress deviators after the elastic step are derived for various viscosity function representations. The resulting solutions of the second-order implicit approximation for the stress deviators of the elastoviscoplastic equations admit passage to the limit as the relaxation time tends to zero. The correcting formulas obtained via this passage to the limit can be treated as regularizers of the numerical solutions to the elastoplastic systems.

Investigation on large-scale 3D seepage characteristics of a pumped-storage power station: a case study in Zhejiang Province, China.

Pumped-storage power stations (PSPSs) have higher requirements for anti-seepage compared with regular power stations. As a result, investigating the seepage distributions of PSPSs is particularly important. However, existing researches remain limited in assessing engineering needs such as ensuring the efficiency of a power station. Taking the Qingyuan PSPS as a typical case, this study aims to investigate the large-scale seepage field distribution while exploring the efficiency of the anti-seepage system. Considering the geological characteristics and structural location, a 3D finite element model is established. Based on the continuous medium model while combined with seepage control measures, the change in leakage while the anti-seepage system failed is further assessed. It is concluded that the operation status of anti-seepage measures will have a certain impact on the leakage volumes of each part. Using a comprehensive assessment, anti-seepage measures can effectively prevent seepage. When failure occurs on anti-seepage curtains, the leakage volume at the corresponding position will show an obvious growth. In summary, the findings of this study highlight the significance of avoiding excessive leakage caused by anti-seepage structure failure, the effective operation of anti-seepage measures must be ensured. The abovementioned results can provide scientific support for the seepage optimization design of PSPSs.

Influence of stone content on face stability for tunnels in sandy cobble strata

As a result of the complex geological conditions of sand-cobble stratum, various types of problems may arise during construction of tunnels crossing sand-cobble stratum, the most prominent of which is the stability problem of the face. In order to study the stability of the tunnel face in sand-cobble stratum, first, a continuous medium model of sandstone soil is established, and numerical simulation is carried out on the three-axis compression test of sandstone soil to analyze its micro-mechanical characteristics. Second, a calculation model of simulated sandstone strata excavation is established by FLAC3D finite difference software. Then, the safety factor K calculated by the strength reduction method is introduced as the evaluation index of the face stability, and the face stability of sand-cobble tunnels with a series of stone content, tunnel burial depth and tunnel diameter are analyzed. The results show that the macro stress-strain curve of sand-cobble soil in the three-axis compression test can be divided into linear stage, elastic-plastic stage and ideal plastic stage, and the shear strength of sand-cobble soil increases with the increase of stone content. In the process of tunnel excavation, the stability of tunnel face increases with the increase of stone content in the stratum; while the tunnel buried depth and diameter increase, the stability of tunnel face decreases. These results provide a reference for predicting the instability and failure of sand-cobble tunnels, which is critical for the construction and safety of tunnels in sand-cobble stratum.

Constitutive Relation Development for Fused Deposition Modeling Three-Dimensional Printing Materials and Simulation of Printing Direction Combination

Abstract Due to the forming or curing process, the materials of three-dimensional (3D) printing have periodic meso-defects, which result in complex constitutive relations and anisotropy. Fused deposition modeling (FDM), which is a typical 3D printing process, inevitably introduces stacking pore defects due to the three-dimensional stacking of materials along the printing direction. At present, research focuses on the mechanical properties of materials printed along only one single direction. To consider the possibility of changing the mechanical properties of materials by adjusting the printing direction, the change in the properties of printing materials along the multiple printing direction combinations was analyzed in this paper. First, based on a continuous medium model, the constitutive model proposed by Garzon-Hernandez et al. was considered, and then to improve the prediction accuracy of the model in the plastic stage, a model describing the porosity change rate of porous materials was introduced to obtain better prediction results. Then, the finite element method (FEM) was developed using the new constitutive relation model implemented by the user defined material subroutine (USERMAT) into ansys software. Second, through the finite element subroutine, the mechanical response of the FDM 3D printing plate with two different printing direction combinations was simulated. The results show that by adjusting the print direction combination of the double-layer FDM 3D printing materials, the materials show a different anisotropy, maximum bearing capacity of tension and shear and buckling resistance.

Simulation of Light Scattering in Automotive Paints: Role of Particle Size

Nowadays, computer simulation is being used to develop new materials. Many of them are dispersed media (e.g., paints, and 3D printer inks). Modern automotive paints are of great interest in research works. They contain colorant particles and thin flat metallic or pearlescent flakes distributed in a clear varnish. There are two main approaches to simulation of light scattering in a dispersed media. The first one is based on the continuous medium model. This model is faster but less accurate. The second approach is the simulation of light propagation through an ensemble of paint flakes and particles represented as an explicit geometry. This model correctly calculates light scattering but is rather time-consuming. In our study, we investigated the dependence of the painted surface luminance on particle size and compared both the approaches. We prove that the effect of coarse particles can emerge even in a model where positions of these particles are not correlated; this is different from the mainstream studies which have only concentrated on the role of these correlations. Then, we suggest a semi-analytical model of dependence on particle size. This model not only allows to more accurately simulate visual appearance but also admits intuitive comprehension of how it is affected by various medium parameters. In case of the divergence between the results of LTE and accurate approaches, we propose a simple approximation that allows to improve the accuracy of the LTE results for coarse particles.

A new numerical well test method of multi-scale discrete fractured tight sandstone gas reservoirs and its application in the Kelasu Gas Field of the Tarim Basin

The cretaceous gas reservoir in Kelasu Gas Field of the Tarim Basin is a rare ultra-deep and ultra-high pressure fractured tight sandstone gas reservoir where multi-scale discrete fractures of matrix, fracture and fault are developed, so its development cannot be conducted just based on static and dynamic reservoir description. In order to solve this problem, this paper establishes a numerical well test model of vertical wells based on matrix, fractures and faults (large fractures and small faults) by combining the random generation of natural fracture networks with the unstructured discrete fracture modeling method to break through the traditional continuous medium well test model. In addition, the model is solved by using the finite element method with mixed element, and the typical well test type curves under different random fracture networks are obtained. And the following research results are obtained. First, based on the observed data, the fracture network distribution modes of fractured tight sandstone gas reservoirs are classified into three categories. The influence of random generation of fracture networks on typical well test type curves is discussed. The results of discrete fracture well test model are compared with those of the traditional continuous medium well test model, and the applicable conditions of the traditional continuous medium well test model is determined. Second, there are great differences between the results of discrete fracture model and those of dual porosity medium model. 1 The dual porosity medium model is a special case of the discrete fracture model, in which the fractures are evenly distributed within infinitely small spacing. Third, the characteristics of well test type curves under three fracture network distribution modes are discussed. The well test type curves that cannot be interpreted by the conventional dual/triple porosity continuous medium model are successfully interpreted by using the established well test interpretation model of random discrete fracture. The curve matching effect is ideal and the interpreted parameters are reasonable. In conclusion, the new model and the new method reveal the development mechanism of step-by-step production and coordinated gas supply between media of different scales, explain the development characteristics of large inter-well productivity difference and abnormal rapid inter-well pressure response, and provide a reference for the development of similar gas reservoirs.

Исследование по динамике многоэтажных зданий

The design of multi-storey buildings is a natural trend in the development of a modern metropolis. Obtaining exact solutions when studying their own and forced oscillations within the framework of a continuous homogeneous medium model (continuum mechanics) with an infinite number of degrees of freedom is often difficult to implement. Therefore, in the article (as part of the modernization of the finite element method), the model of a multi-storey building is discretized and endowed with a finite number of degrees of freedom placed in the middle of the finite elements at the nodes (the mass of finite elements is also placed there), which elastically interact with the finite elements of the model that do not have mass. It is believed that the elements of a multi-storey building work only for bending, which is fully justified by comparing the frequencies of its bending and longitudinal oscillations. The resolving system of differential equations of oscillations of a multi-storey building, in which expressions for energies (potential, kinetic and Rayleigh) are written in quadratures, is obtained using Lagrange equations of the second kind. In the article, the problems of free oscillations of 3- and 100-storey buildings are solved using Green’s functions, stiffness, mass, compliance matrices, etc. The approximate results obtained in the article, when compared with the little-known approximate results obtained by other methods, as well as exact results (direct and indirect methods of boundary elements), showed a good correspondence.

Двойственная вариационная модель стационарного процесса теплопроводности, учитывающая пространственную нелокальность

Microcontinuum theories boast a great potential for simulating structurally sensitive materials. There exists a sufficiently large number of works delineating the basics of non-local mechanics using the theory of elasticity as an example. Estimating the investigative capacity of non-local mechanics is at present particularly relevant to simulating nanodevices, nanoelectromechanical systems (NEMS), and media featuring complex internal micro- and nanostructures. Typically, analysing these simulations involves overcoming certain difficulties caused by the necessity to solve integro-differential equations numerically. Variational methods may be successfully applied to analysing mathematical models of continuous media as an additional tool. The paper describes plotting an alternative functional for the problem of steady-state thermal conductivity in a homogeneous body, taking into account non-locality effects and featuring a temperature-independent thermal conductivity coefficient. We show that the stationary conditions for this functional do not differ from those in the absence of non-locality. The alternative functional combined with the fundamental functional presented previously constitute a dual variational model. We quantitatively analyse the problem of an infinite planar plate featuring constantly active internal heat sources. The dual variational formulation of the problem allows us not only to obtain an approximate solution to the problem under consideration, but also to estimate its error, as well as to reduce this error by selecting other approximating functions if necessary

Numerical simulation of the heat production potential of Guide Basin in China considering the heterogeneity and anisotropy of the reservoir

Understanding heat production performance is crucial for the development and utilization of geothermal reservoirs. This study investigates the heat production characteristics of a geothermal heating system in naturally fractured reservoirs of the Guide Basin in China while considering the heterogeneity and anisotropy of the reservoir. A 3D discrete fracture network (DFN) model is established based on the fracture information obtained from Guide Basin and then the permeability at different locations in the model is calculated. Finally, the calculated permeability is used to analyze heat production performance using TOUGH2. The results indicate the cumulative heat production in 40 years is 987 GWh, which is equivalent to the heat produced by 1.48×108 kg of standard coal. The proposed methodology, which considers the heterogeneity and anisotropy of the reservoir, combines the advantages of the DFN model and continuous medium model and can be used to analyze other geothermal reservoirs.

Numerical Simulation of the Ionization Wave Front in Xe in the Local Energy Approximation of a Continuous Medium Model

Numerical Simulation of the Ionization Wave Front in Xe in the Local Energy Approximation of a Continuous Medium Model

Tailored nanophononic wavefield in a patterned bilayer system probed by ultrafast convergent beam electron diffraction

Optically excited nanostructures provide a versatile platform for the generation of confined nanophononic fields with potential (non-)linear interactions between different degrees of freedom. Control of resonance frequencies and the selective excitation of acoustic modes still remains challenging due to the interplay of nanoscale geometries and interfacial coupling mechanisms. Here, we demonstrate that a semiconductor membrane patterned with a platinum stripe acts as a tailored source for high-frequency strain waves generating a multi-modal distortion wave propagating through the membrane. To locally monitor the ultrafast structural dynamics at a specific distance from the deposited metal stripe, we employ ultrafast convergent beam electron diffraction in a laser-pump/electron-probe scheme. Experimentally observed acoustic deformations are reproduced by numerical simulations in a continuous medium model, revealing a spatiotemporal evolution of the lattice dynamics dominated by local rotations with minor strain and shear contributions.

Mathematical modeling of temperature stresses in a nonlocal thermoviscoelastic continuous medium

The improvement of the properties of structural and functional materials is associated with the synthesis of materials from structures with limiting values of properties (for example, extremely strong, refractory, thermostable, etc.). Such materials have an inhomogeneous structure, justified by the technological features of their preparation. In recent years, such materials have come to be called “structure–sensitive,” and the study of their thermomechanical characteristics has become possible within the framework of generalized mechanics of a continuous medium. Mathematical models describing such materials belong to the class of non-local models proposed by A. K. Ehringen. Now, there are few works on the use of nonlocal viscoelasticity, while many materials exhibit viscoelastic properties, even nonlocal viscoelastic properties, for example, solid propellants, composite materials, etc. The paper considers a mathematical model of a nonlocal thermoviscoelastic continuous medium. Using the finite element method, the temperature stress distributions are found for high-intensity pulsed heating of a nonlocal half-space.

Sub-arcsecond LOFAR imaging of Arp 299 at 150 MHz

Context. Arp 299 is the brightest luminous infrared galaxy (LIRG) within 50 Mpc, with IR luminosity log(LIR∕L⊙) = 11.9. It provides a unique laboratory for testing physical processes in merging galaxies. Aims. We study for the first time the low-frequency (~150 MHz) radio brightness distribution of Arp 299 at subarcsecond resolution, tracing in both compact and extended emission regions the local spectral energy distribution (SED) in order to characterize the dominant emission and absorption processes. Methods. We analysed the spatially resolved emission of Arp 299 revealed by 150 MHz international baseline Low-Frequency Array (LOFAR) and 1.4, 5.0, and 8.4 GHz Very Large Array (VLA) observations. Results. We present the first subarcsecond (0.4″ ~ 100 pc) image of the whole Arp 299 system at 150 MHz. The high surface brightness sensitivity of our LOFAR observations (~100 μJy beam−1) allowed us to detect all of the nuclear components detected at higher frequencies, as well as the extended steep-spectrum emission surrounding the nuclei. We obtained spatially resolved, two-point spectral index maps for the whole galaxy: the compact nuclei show relatively flat spectra, while the extended, diffuse component shows a steep spectrum. We fitted the radio SED of the nuclear regions using two different models: a continuous free-free medium model and a clumpy model. The continuous model can explain the SED of the nuclei assuming a population of relativistic electrons subjected to synchrotron, bremsstrahlung, and ionization losses. The clumpy model fits assuming relativistic electrons with negligible energy losses, and thermal fractions that are more typical of star-forming galaxies than those required for the continuous model. Conclusions. Our results confirm the usefulness of combining spatially resolved radio imaging at both MHz and GHz frequencies to characterize in detail the radio emission properties of LIRGs from the central 100 pc out to the kiloparsec galaxy-wide scales.