scholarly journals MODELING OF PRODUCING PRESSURE IN HETEROGENEOUS OIL-BEARING RESERVOIRS

2021 ◽  
pp. 72-79
Author(s):  
Mikhail Lubkov ◽  
Oksana Zakharchuk ◽  
Viktoriia Dmytrenko ◽  
Oleksandr Petrash
Keyword(s):  
Finite Element ◽  
Difference Method ◽  
Stationary Problem ◽  
Injection Well ◽  
Practical Significance ◽  
The Finite Element Method ◽  
Oil Viscosity ◽  
Injection Wells ◽  
Remote Zone ◽  
Close Relationship

Numerical modeling of the distribution of the reservoir pressure drop in the vicinity of an operating well was carried out taking into account the inhomogeneous distribution of filtration characteristics (permeability and oil viscosity) in the near and distant zones of the well operation in order to study the practical aspects of filtration in heterogeneous oil-bearing formations based on a combined finite-element-difference method for non-stationary problem of piezoconductivity. The use of the combined finite-element-difference method enables to combine the advantages of the finite-element method and the finite difference method: to model geometrically complex areas, to find the value at any point of the object under study, while the implicit difference scheme. It is shown that the intensity of filtration processes in the vicinity of the operating well depends mainly on the permeability, and, to a lesser extent, on the viscosity of the oil. Moreover, the influence of the permeability of the oil phase in the remote zone (Rd < 5 m) is greater than the effect in the close zone (Rd > 5 m) of the operating well. In the case of low permeability of the oil phase in the vicinity of the existing well, to maintain stable oil production, it is necessary to place an injection well near the production well. Using the method suggested, it is possible to predict the effect of the injection well on the formation pressure distribution in the formation. The scientific novelty of the work lies in the study of the influence of the heterogeneous permeability and oil viscosity distribution on the reservoir pressures distribution around the wells by modeling filtration processes based on a combined finite-element-difference method. The practical significance of the research results comes down to confirming the close relationship between the heterogeneity of the porous medium and the reservoir pressures distribution around an operating producing well. The combined finite-element-difference method used in this work can be used to solve other filtration problems (for example, to calculate the gas saturation of a reservoir, create a method for calculating well flow rates, assess the effect of injection wells on filtration processes).

scholarly journals Investigation of the influence of the heterogeneous permeability distribution on the oil phase displacement processes

2021 ◽  
Vol 5 (1(61)) ◽  
pp. 33-40
Author(s):  
Miсhail Lubkov ◽  
Oksana Zakharchuk ◽  
Viktoriia Dmytrenko ◽  
Oleksandr Petrash
Keyword(s):  
Finite Element ◽  
Difference Method ◽  
High Reliability ◽  
Oil Field ◽  
Injection Well ◽  
Shear Direction ◽  
Reservoir Pressure ◽  
Filtration Process ◽  
Injection Wells ◽  
The Impact

The object of research is the filtration processes of displacement of the oil phase under the influence of an injection well in a heterogeneous porous medium. It is possible to evaluate and take into account the effect of reservoir heterogeneity on the distribution of reservoir pressure (and, consequently, on the intensity of the filtration process) using numerical modeling of filtration processes based on the piezoelectric equation. To solve the non-stationary anisotropic problem of piezoconductivity, it is proposed to apply the combined finite-element-difference method of M. Lubkov, which makes it possible to take into account the inhomogeneous distribution of permeability inside the anisotropic oil-bearing formation and at its boundaries, and to adequately calculate the distribution of reservoir pressure. The use of the combined finite-element-difference method allows to combine the advantages of the finite-element method and the finite difference method: to model geometrically complex areas, to find the value at any point of the object under study. At the same time, the use of an implicit difference scheme when finding the nodal values of the grid provides high reliability and convergence of the results. The simulation results show that the distribution of the pressure field between the production and injection wells significantly depends on their location, both in the isotropic landslide and in the anisotropic oil-bearing reservoir. It is shown that the distance between the wells of more than 1 km levels out the effectiveness of the impact of the injection well on the oil filtration process. The influence of the permeability of the oil phase in the shear direction dominates the influence of the permeability in the axial directions (affects the pressure decrease by 4–9.5 %). In the case of a landslide-isotropic reservoir, the wells should be located in the shear (diagonal) direction, which will provide the lowest level of drop in the average reservoir pressure (by 4 %). Based on the information obtained, for the effective use of anisotropic low-permeability formations, it is necessary to place production and injection wells in areas with relatively low anisotropy of the formation permeability, especially to avoid places with the presence of landslide permeability of the formation. The location of the wells is important so that, on the one hand, there is no blockage of oil from the side of reduced permeability, and on the other hand, rapid depletion of the formation from the side of increased permeability does not occur. And also the mutual exchange between the production and injection wells did not stop. When placing a system of production and injection wells in anisotropic formations of an oil field, it is necessary to carry out a systematic analysis of the surrounding anisotropy of the formations in order to place them in such a way that would ensure effective dynamics of filtration processes around these wells. Using the method used, it is possible to predict the impact of an injection well on the distribution of reservoir pressure in the reservoir.

Computer simulation of optical radiation scattering by aerosol media

2020 ◽  
Vol 86 (8) ◽  
pp. 43-48
Author(s):  
V. V. Semenov
Keyword(s):  
Finite Element Method ◽  
Computer Simulation ◽  
Finite Element ◽  
Optical Radiation ◽  
Light Transmission ◽  
Initial Conditions ◽  
Practical Significance ◽  
The Finite Element Method ◽  
Dispersed Medium ◽  
Element Method

Development of the technologies simulating optical processes in an arbitrary dispersed medium is one of the important directions in the field of optical instrumentation and can provide computer simulation of the processes instead of using expensive equipment in physical experiments. The goal of the study is simulation of scattering of optical radiation by aerosol media using the finite element method to show a practical significance of the results of virtual experiments. We used the following initial conditions of the model: radius of a spherical particle of distilled water is 1 μm, wavelength of the incident optical radiation is 0.6328 μm, air is a medium surrounding the particle. An algorithm for implementation of the model by the finite element method is proposed. A subprogram has been developed which automates a virtual experiment for a group of particles to form their random arrangement in the model and possibility of changing their geometric shape and size within predetermined intervals. Model dependences of the radiation intensity on the scattering angle for single particle and groups of particles are presented. Simulation of the light transmission through a dispersed medium provides development of a given photosensor design and determination of the minimum number of photodetectors when measuring the parameters of the medium under study via analysis of the indicatrix of scattering by a group of particles.

scholarly journals Comparative analysis of the results of determining the parameters of the stress-strain state of equal slope shell

2019 ◽  
Vol 15 (5) ◽  
pp. 374-383
Author(s):  
Vyacheslav N. Ivanov ◽  
Olga O. Alyoshina
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Difference Method ◽  
Strain State ◽  
The Finite Element Method ◽  
Stress Strain ◽  
Slope Shell ◽  
Stress Strain State ◽  
Variational Difference Method ◽  
Element Method

Relevance. Thin-walled structures of shells constitute a large class in architecture, in civil and industrial construction, mechanical engineering and instrument making, aircraft, rocket and shipbuilding, etc. Each surface has certain ad-vantages over the other. So the torso surface can be deployed on the plane of all its points without folds and breaks, with the length of the curves and the angles between any curves belonging to the surface, do not change. The investigation of the stressstrain state of the equal slope shell with a director ellipse at the base is presented to date in a small volume. The aim of the work. Obtaining data for comparative analysis of the results of the stress-strain state of equal slope shells by the finite element method and the variational-difference method. Methods. To assess the stressstrain state of the equal slope shell, the SCAD Office computer complex based on the finite element method and the “PLATEVRM” program, written on the basis of the variational-difference method, are used. Results. The numerical results of the stress-strain state of the equal slope shell are obtained and analyzed, the pros and cons of the results of calculations by the finite element method and the variational-difference method are revealed.

scholarly journals The optimal dimensions of the domain for solving the single-band Schrödinger equation by the finite-difference and finite-element methods

2014 ◽  
Vol 11 (1) ◽  
pp. 73-84 ◽  
Author(s):  
Dusan Topalovic ◽  
Stefan Pavlovic ◽  
Nemanja Cukaric ◽  
Milan Tadic
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Finite Element Methods ◽  
Ground State ◽  
Difference Method ◽  
Grid Size ◽  
The Finite Element Method ◽  
The Finite Difference Method

The finite-difference and finite-element methods are employed to solve the one-dimensional single-band Schr?dinger equation in the planar and cylindrical geometries. The analyzed geometries correspond to semiconductor quantum wells and cylindrical quantum wires. As a typical example, the GaAs/AlGaAs system is considered. The approximation of the lowest order is employed in the finite-difference method and linear shape functions are employed in the finite-element calculations. Deviations of the computed ground state electron energy in a rectangular quantum well of finite depth, and for the linear harmonic oscillator are determined as function of the grid size. For the planar geometry, the modified P?schl-Teller potential is also considered. Even for small grids, having more than 20 points, the finite-element method is found to offer better accuracy than the finite-difference method. Furthermore, the energy levels are found to converge faster towards the accurate value when the finite-element method is employed for calculation. The optimal dimensions of the domain employed for solving the Schr?dinger equation are determined as they vary with the grid size and the ground-state energy.

Finite-Difference Method Appliance to the Computation of Ground Additional Stress and Settlement of Storage Tank

2011 ◽  
Vol 243-249 ◽  
pp. 2638-2642
Author(s):  
Xu Dong Cheng ◽  
Wen Shan Peng ◽  
Lei Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Storage Tank ◽  
Three Dimensional ◽  
Additional Stress ◽  
The Finite Element Method ◽  
The Finite Difference Method

This paper adopts the Finite-difference method to research the distribution of ground additional stress and distortion in differently isotropic and non-isotropic foundation conditions, and uses the Finite-difference method to compare with the Finite-element method and the three-dimensional settlement method used by the code. Through comparative analysis, the reliability and superiority of Finite-difference method used for calculating ground additional stress and settlement are justified.

scholarly journals A study of vectorization for matrix-free finite element methods

2020 ◽  
Vol 34 (6) ◽  
pp. 629-644
Author(s):  
Tianjiao Sun ◽  
Lawrence Mitchell ◽  
Kaushik Kulkarni ◽  
Andreas Klöckner ◽  
David A Ham ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
High Performance ◽  
Practical Significance ◽  
Peak Performance ◽  
The Finite Element Method ◽  
Wide Range ◽  
Local Assembly ◽  
Matrix Free ◽  
Element Method

Vectorization is increasingly important to achieve high performance on modern hardware with SIMD instructions. Assembly of matrices and vectors in the finite element method, which is characterized by iterating a local assembly kernel over unstructured meshes, poses difficulties to effective vectorization. Maintaining a user-friendly high-level interface with a suitable degree of abstraction while generating efficient, vectorized code for the finite element method is a challenge for numerical software systems and libraries. In this work, we study cross-element vectorization in the finite element framework Firedrake via code transformation and demonstrate the efficacy of such an approach by evaluating a wide range of matrix-free operators spanning different polynomial degrees and discretizations on two recent CPUs using three mainstream compilers. Our experiments show that our approaches for cross-element vectorization achieve 30% of theoretical peak performance for many examples of practical significance, and exceed 50% for cases with high arithmetic intensities, with consistent speed-up over (intra-element) vectorization restricted to the local assembly kernels.

The Definition of a Critical Deflection of Compressed Rods with the Creep by the Method of Bubnov-Galerkin

2018 ◽  
Vol 931 ◽  
pp. 127-132
Author(s):  
Batyr M. Yazyev ◽  
Serdar B. Yazyev ◽  
Anatoly P. Grinev ◽  
Elena A. Britikova
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Methods ◽  
Difference Method ◽  
Stability Problem ◽  
The Finite Element Method ◽  
The Difference ◽  
The Stability ◽  
Definition Of ◽  
The Galerkin Method

The comparison of the numerical methods: the finite element method, the Galerkin Method, the difference method is considered for the study of the stability of the rods. The dependence of the solution of the stability problem on the parameters of the discretization of these numerical methods is studied. It is shown that the mathematical models are sufficiently accurate to analyze the stability of the rods of constant and variable sections.

Finite Element Analysis of Single Dust-Colleting Plate’s Rapping Acceleration

2012 ◽  
Vol 518-523 ◽  
pp. 2526-2529
Author(s):  
Qi Ming Xiao ◽  
Ke Shu Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Electrostatic Precipitator ◽  
New Method ◽  
Practical Significance ◽  
The Finite Element Method ◽  
Element Analysis ◽  
Dynamic Display ◽  
Calculation Results ◽  
Element Method

Electrostatic precipitator is a kind of important dust collecting equipment. The rapping acceleration is the standard of electrostatic precipitator design and manufacturing. The aim of the work reported in this paper was find a new method for solving the rapping acceleration. Based on the numerical analytical method and the dynamic display algorithm, this paper is to build a new method for solving the rapping acceleration of electrostatic precipitator by using finite element method. By comparing the results of finite element method and the model test data and analyzing calculation results, this method is proved to be correct and effective. Using this method in the analyzing of practical equipment, the result basically tallies with the actual result. The finite element method can be used conveniently in different plate profiles, different ways of hanging, striking hammers and different methods of rapping. So the finite element method has an important practical significance in the analyzing of existing plate and the researching of new plate.

scholarly journals On Nonlocal Computation of Eigenfrequencies of Beams Using Finite Difference and Finite Element Methods

2015 ◽  
Vol 15 (07) ◽  
pp. 1540008 ◽  
Author(s):  
Noël Challamel ◽  
Vincent Picandet ◽  
Issac Elishakoff ◽  
Chien Ming Wang ◽  
Bernard Collet ◽  
...  
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Gradient Elasticity ◽  
The Finite Element Method ◽  
Finite Difference Equations ◽  
Potential Applications ◽  
Dynamics Problems ◽  
Numerical Approaches

In this paper, we show that two numerical methods, specifically the finite difference method and the finite element method applied to continuous beam dynamics problems, can be asymptotically investigated by some kind of enriched continuum approach (gradient elasticity or nonlocal elasticity). The analysis is restricted to the vibrations of elastic beams, and more specifically the computation of the natural frequencies for each numerical method. The analogy between the finite numerical approaches and the equivalent enriched continuum is demonstrated, using a continualization procedure, which converts the discrete numerical problem into a continuous one. It is shown that the finite element problem can be transformed into a system of finite difference equations. The convergence rate of the finite numerical approaches is quantified by an equivalent Rayleigh's quotient. We also present some exact analytical solutions for a first-order finite difference method, a higher-order finite difference method or a cubic Hermitian finite element, valid for arbitrary number of nodes or segments. The comparison between the exact numerical solution and the approximated nonlocal approaches shows the efficiency of the continualization methodology. These analogies between enriched continuum and finite numerical schemes provide a new attractive framework for potential applications of enriched continua in computational mechanics.

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