Dual-Porosity Dual-Permeability Poroelastodynamics Analytical Solutions for Mandel’s Problem

2020 ◽  
Vol 88 (1) ◽  
Author(s):  
Chao Liu
Keyword(s):  
Analytical Solutions ◽  
Rock Sample ◽  
Numerical Algorithms ◽  
Harmonic Excitation ◽  
Dual Porosity ◽  
Rock Matrix ◽  
Low Frequencies ◽  
Resonance Frequencies ◽  
Special Cases ◽  
Naturally Fractured

Abstract Analytical solutions to the classical Mandel’s problem play an important role in understanding Biot’s theory of poroelasticity and validating geomechanics numerical algorithms. In this paper, existing quasi-static poroelastic solutions to this problem are extended to the dual-porosity dual-permeability poroelastodynamics solution which considers inertial effects for a naturally fractured and fluid-saturated sample subjected to a harmonic excitation. The solution can generate the associated elastodynamics and poroelastodynamics solutions as special cases. A naturally fractured Ohio sandstone is selected to demonstrate the newly derived solution. The elastodynamics, poroelastodynamics, and dual-porosity poroelastodynamics solutions are compared to illustrate the effects of fluid–solid coupling and the natural fractures. The rock sample behaves in drained condition at low frequencies when the oscillation has insignificant impedance effects on fluid movement. Compared to the other two solutions, the dual-porosity solution predicts the largest amplitude of displacement at low frequencies when the response is predominantly controlled by the stiffness. The Mandel–Cryer effect is observed in both rock matrix and fractures and occurs at a lower frequency in rock matrix because it is easier to build up pore pressure in lower-permeability rock matrix. At high frequencies, pore fluids are trapped and the rock sample behaves in an undrained state. At the resonance frequencies, the elastodynamics solution provides the largest amplitude of displacement, followed by the poroelastodynamics and dual-porosity poroelastodynamics solution. This is because of the dissipation caused by the presence of both fluid and fractures.

Theory and Analytical Solutions to Coupled Processes of Transport and Deformation in Dual-Porosity Dual-Permeability Poro-Chemo-Electro-Elastic Media

2018 ◽  
Vol 85 (11) ◽  
Author(s):  
Chao Liu ◽  
Amin Mehrabian ◽  
Younane N. Abousleiman
Keyword(s):  
Analytical Solutions ◽  
Fluid Pressure ◽  
Pore Fluid ◽  
Dual Porosity ◽  
Coupled Processes ◽  
Electrical Potentials ◽  
Solid Deformation ◽  
Special Cases ◽  
Time Variations ◽  
Electrically Charged

The linear theory of dual-porosity and dual-permeability poro-chemo-electro-elasticity is presented. The theory outlines the dual-continuum formulation of multiple coupled processes involving solid deformation, pore fluid flow, and electrically charged species transport, within and in between two coexisting porosity systems of a fluid-saturated, poro-elastic medium. The described formulation is used to derive the analytical solutions to the inclined wellbore problem and axisymmetric Mandel-Type problem of dual-porosity, dual-permeability poro-chemo-electro-elasticity. The effects of chemical and electrical potentials on the distributions of stress and pore pressure are demonstrated by numerical examples pertaining to the considered problems. It is shown that the fully coupled nature of the solutions rigorously captures the seemingly anomalous time variations of the effective stress as driven by the pore fluid pressure disturbances, as well as the distribution and movement of anions/cations within the dual-porosity porous medium. The existing subset of published solutions on the subject is successfully reproduced as special cases of the solutions presented in this paper.

scholarly journals Analytical Investigation of Viscoelastic Stagnation-Point Flows with Regard to Their Singularity

2021 ◽  
Vol 11 (15) ◽  
pp. 6931
Author(s):  
Jie Liu ◽  
Martin Oberlack ◽  
Yongqi Wang
Keyword(s):  
Stress Distribution ◽  
Stress Field ◽  
Stagnation Point ◽  
Analytical Solutions ◽  
Wide Spectrum ◽  
Momentum Conservation ◽  
Stagnation Point Flow ◽  
Model Parameters ◽  
Viscoelastic Models ◽  
Special Cases

Singularities in the stress field of the stagnation-point flow of a viscoelastic fluid have been studied for various viscoelastic constitutive models. Analyzing the analytical solutions of these models is the most effective way to study this problem. In this paper, exact analytical solutions of two-dimensional steady wall-free stagnation-point flows for the generic Oldroyd 8-constant model are obtained for the stress field using different material parameter relations. For all solutions, compatibility with the conservation of momentum is considered in our analysis. The resulting solutions usually contain arbitrary functions, whose choice has a crucial effect on the stress distribution. The corresponding singularities are discussed in detail according to the choices of the arbitrary functions. The results can be used to analyze the stress distribution and singularity behavior of a wide spectrum of viscoelastic models derived from the Oldroyd 8-constant model. Many previous results obtained for simple viscoelastic models are reproduced as special cases. Some previous conclusions are amended and new conclusions are drawn. In particular, we find that all models have singularities near the stagnation point and most of them can be avoided by appropriately choosing the model parameters and free functions. In addition, the analytical solution for the stress tensor of a near-wall stagnation-point flow for the Oldroyd-B model is also obtained. Its compatibility with the momentum conservation is discussed and the parameters are identified, which allow for a non-singular solution.

Upgraded Railway Front Searchlight Design Plastic Deformations by its Vibrations with Resonance Frequencies

2016 ◽  
Vol 684 ◽  
pp. 111-119 ◽  
Author(s):  
Stanislav Rafaelevich Abulkhanov ◽  
Dmitrii Sergeevich Goryainov
Keyword(s):  
Natural Frequencies ◽  
Ansys Software ◽  
Software Environment ◽  
Low Frequencies ◽  
Plastic Deformations ◽  
Vibration Resistance ◽  
First Case ◽  
Resonance Frequencies ◽  
The One ◽  
Electric Lamp

Natural frequencies of the four upgraded front searchlight designs were received in ANSYS software environment. In the first case serial front searchlight incandescent electric lamp was replaced by a LED group which was mounted on the one-piece cylinder backing. The second front searchlight design had the backing which was upgraded by a radial ribs and concentric rigidity ferrules. Analyze of the backing deformation character by vibrations with the natural frequencies established a number of design solutions which make it possible to raise front searchlight vibration resistance. By the front searchlight model were established that the natural frequencies of the searchlight with the one-piece backing appertain to the whole range of the train vibrations. Natural frequencies of the backing with perforation, rigidity ferrules, and radial ribs appertain to the low frequencies of the railway locomotive vibrations spectrum. On basis of devised methodology of analyze of the deformation and natural frequencies of the surface carrying a LED group the vibration-proof searchlight design was introduced and researched.

Optimization of spiral-shaped piezoelectric energy harvester using Taguchi method

2017 ◽  
Vol 24 (19) ◽  
pp. 4484-4491 ◽  
Author(s):  
R Tikani ◽  
L Torfenezhad ◽  
M Mousavi ◽  
S Ziaei-Rad
Keyword(s):  
Taguchi Method ◽  
Energy Harvester ◽  
Piezoelectric Materials ◽  
Mechanical Energy ◽  
Experimental Investigations ◽  
Optimum Level ◽  
Low Frequencies ◽  
Piezoelectric Energy ◽  
Resonance Frequencies ◽  
Design Values

Nowadays, environmental energy resources, especially mechanical vibrations, have attracted the attention of researchers to provide energy for low-power electronic circuits. A common method for environmental mechanical energy harvesting involves using piezoelectric materials. In this study, a spiral multimode piezoelectric energy harvester was designed and fabricated. To achieve wide bandwidth in low frequencies (below 15 Hz), the first three resonance frequencies of the beam were designed to be close to each other. To do this, the five lengths of the substrate layer were optimized by the Taguchi method, using an L27 orthogonal array. Each experiment of the Taguchi method was then simulated in ANSYS software. Next, the optimum level of each design variable was obtained. A test rig was then constructed based on the optimum design values and some experimental investigations were conducted. A good correlation was observed between measured and the finite element results.

scholarly journals Dynamic Analytical Solution of a Piezoelectric Stack Utilized in an Actuator and a Generator

2018 ◽  
Vol 8 (10) ◽  
pp. 1779 ◽  
Author(s):  
Xinnan Liu ◽  
Jianjun Wang ◽  
Weijie Li
Keyword(s):  
Analytical Solution ◽  
Dynamic Characteristics ◽  
Analytical Solutions ◽  
External Load ◽  
Piezoelectric Actuators ◽  
Displacement Method ◽  
Proposed Model ◽  
Special Cases ◽  
Piezoelectric Stacks ◽  
Comprehensive Manner

This paper presents the dynamic analytical solution of a piezoelectric stack utilized in an actuator and a generator based on the linear piezo-elasticity theory. The solutions for two different kinds of piezoelectric stacks under external load were obtained using the displacement method. The effects of load frequency and load amplitude on the dynamic characteristics of the stacks were discussed. The analytical solutions were validated using the available experimental results in special cases. The proposed model is able not only to predict the output properties of the devices, but also to reflect the inner electrical and mechanical components, which is helpful for designing piezoelectric actuators and generators in a comprehensive manner.

Pressure-Transient Tests and Flow Regimes in Fractured Reservoirs

2015 ◽  
Vol 18 (02) ◽  
pp. 187-204 ◽  
Author(s):  
Fikri Kuchuk ◽  
Denis Biryukov
Keyword(s):  
History Matching ◽  
Fractured Reservoirs ◽  
Flow Regimes ◽  
Naturally Fractured Reservoirs ◽  
Dual Porosity ◽  
Hydraulic Fractures ◽  
Fractured Reservoir ◽  
Pressure Transient ◽  
Matrix Block ◽  
Naturally Fractured

Summary Fractures are common features in many well-known reservoirs. Naturally fractured reservoirs include fractured igneous, metamorphic, and sedimentary rocks (matrix). Faults in many naturally fractured carbonate reservoirs often have high-permeability zones, and are connected to numerous fractures that have varying conductivities. Furthermore, in many naturally fractured reservoirs, faults and fractures can be discrete (rather than connected-network dual-porosity systems). In this paper, we investigate the pressure-transient behavior of continuously and discretely naturally fractured reservoirs with semianalytical solutions. These fractured reservoirs can contain periodically or arbitrarily distributed finite- and/or infinite-conductivity fractures with different lengths and orientations. Unlike the single-derivative shape of the Warren and Root (1963) model, fractured reservoirs exhibit diverse pressure behaviors as well as more than 10 flow regimes. There are seven important factors that dominate the pressure-transient test as well as flow-regime behaviors of fractured reservoirs: (1) fractures intersect the wellbore parallel to its axis, with a dipping angle of 90° (vertical fractures), including hydraulic fractures; (2) fractures intersect the wellbore with dipping angles from 0° to less than 90°; (3) fractures are in the vicinity of the wellbore; (4) fractures have extremely high or low fracture and fault conductivities; (5) fractures have various sizes and distributions; (6) fractures have high and low matrix block permeabilities; and (7) fractures are damaged (skin zone) as a result of drilling and completion operations and fluids. All flow regimes associated with these factors are shown for a number of continuously and discretely fractured reservoirs with different well and fracture configurations. For a few cases, these flow regimes were compared with those from the field data. We performed history matching of the pressure-transient data generated from our discretely and continuously fractured reservoir models with the Warren and Root (1963) dual-porosity-type models, and it is shown that they yield incorrect reservoir parameters.

scholarly journals Active Vibration Control of a Nonlinear Beam with Self- and External Excitations

2013 ◽  
Vol 20 (6) ◽  
pp. 1033-1047 ◽  
Author(s):  
J. Warminski ◽  
M. P. Cartmell ◽  
A. Mitura ◽  
M. Bochenski
Keyword(s):  
Analytical Solutions ◽  
Order Approximation ◽  
Equations Of Motion ◽  
Active Vibration Control ◽  
Harmonic Excitation ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Nonlinear Beam ◽  
Approximate Analytical Solutions ◽  
Full Structure

An application of the nonlinear saturation control (NSC) algorithm for a self-excited strongly nonlinear beam structure driven by an external force is presented in the paper. The mathematical model accounts for an Euler-Bernoulli beam with nonlinear curvature, reduced to first mode oscillations. It is assumed that the beam vibrates in the presence of a harmonic excitation close to the first natural frequency of the beam, and additionally the beam is self-excited by fluid flow, which is modelled by a nonlinear Rayleigh term for self-excitation. The self- and externally excited vibrations have been reduced by the application of an active, saturation-based controller. The approximate analytical solutions for a full structure have been found by the multiple time scales method, up to the first-order approximation. The analytical solutions have been compared with numerical results obtained from direct integration of the ordinary differential equations of motion. Finally, the influence of a negative damping term and the controller's parameters for effective vibrations suppression are presented.

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