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.

ON THE DEPENDENCE OF THE ELASTIC PROPERTIES OF A POROUS ROCK ON THE COMPRESSIBILITY OF THE PORE FLUID

Geophysics ◽  
1975 ◽  
Vol 40 (4) ◽  
pp. 608-616 ◽  
Author(s):  
Robert J. S. Brown ◽  
Jan Korringa
Keyword(s):  
Elastic Properties ◽  
Volume Fraction ◽  
Fluid Pressure ◽  
Reciprocity Theorem ◽  
Pore Fluid ◽  
Pore System ◽  
Porous Rock ◽  
Special Cases ◽  
The One ◽  
Interconnected Pore

An equation is derived for the dependence of the elastic properties of a porous material on the compressibility of the pore fluid. More generally, the elastic properties of a container of arbitrary shape are related to the compressibility of the fluid filling a cavity in the container. If the pore system or cavity under consideration is filled with a fluid of compressibility [Formula: see text], the compressibility κ* of the closed container is given by [Formula: see text] Here [Formula: see text] is the compressibility of the container with the fluid pressure held constant in the interconnected pore system or cavity. Fluids in other pores or cavities not connected with the one in question contribute to the value of [Formula: see text]. ϕ is the porosity, i.e., the volume fraction corresponding to the pore system or cavity in question. The equation contains two distinct effective compressibilities, [Formula: see text] and [Formula: see text], of the material exclusive of the pore fluid. When this material is homogeneous, one has [Formula: see text], and the equation reduces to a well‐known relation by Gassmann. For the other elastic properties, we also obtain expressions which generalize Gassmann’s work and which also differ from it only in the appearance of [Formula: see text] instead of [Formula: see text] in one term. Our result is intimately related to the reciprocity theorem of elasticity. Special cases are discussed.

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.

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.

scholarly journals Correction to: Stress and pore fluid pressure control of seismicity rate changes following the 2016 Kumamoto earthquake, Japan

2021 ◽  
Vol 73 (1) ◽  
Author(s):  
Kodai Nakagomi ◽  
Toshiko Terakawa ◽  
Satoshi Matsumoto ◽  
Shinichiro Horikawa
Keyword(s):  
Fluid Pressure ◽  
Pressure Control ◽  
Pore Fluid ◽  
2016 Kumamoto Earthquake ◽  
Pore Fluid Pressure ◽  
Seismicity Rate ◽  
Kumamoto Earthquake ◽  
The 2016 Kumamoto Earthquake ◽  
Seismicity Rate Changes

An amendment to this paper has been published and can be accessed via the original article.

Anisotropic Porochemoelectroelastic Solution for an Inclined Wellbore Drilled in Shale

2013 ◽  
Vol 80 (2) ◽  
Author(s):  
Minh H. Tran ◽  
Younane N. Abousleiman
Keyword(s):  
Porous Media ◽  
Fluid Pressure ◽  
Transversely Isotropic ◽  
Biological Tissues ◽  
Analytical Models ◽  
Combined Effects ◽  
Saturated Porous Media ◽  
Stress Distributions ◽  
Shale Formations ◽  
Electrically Charged

The porochemoelectroelastic analytical models have been used to describe the response of chemically active and electrically charged saturated porous media such as clay soils, shales, and biological tissues. However, existing studies have ignored the anisotropic nature commonly observed on these porous media. In this work, the anisotropic porochemoelectroelastic theory is presented. Then, the solution for an inclined wellbore drilled in transversely isotropic shale formations subjected to anisotropic far-field stresses with time-dependent down-hole fluid pressure and fluid activity is derived. Numerical examples illustrating the combined effects of porochemoelectroelastic behavior and anisotropy on wellbore responses are also included. The analysis shows that ignoring either the porochemoelectroelastic effects or the formation anisotropy leads to inaccurate prediction of the near-wellbore pore pressure and effective stress distributions. Finally, wellbore responses during a leak-off test conducted soon after drilling are analyzed to demonstrate the versatility of the solution in simulating complex down-hole conditions.

Approximate analytical solution for the propagation of shock wave in a mixture of small solid particles and non-ideal gas: isothermal flow

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Gorakh Nath
Keyword(s):  
Shock Wave ◽  
Analytical Solutions ◽  
Order Approximation ◽  
Fluid Pressure ◽  
Strong Shock ◽  
Cylindrical Symmetry ◽  
Solid Particles ◽  
Approximate Analytical Solutions ◽  
Axis Of Symmetry ◽  
Physical Variables

Abstract This paper presents the development of mathematical model to obtain the approximate analytical solutions for isothermal flows behind the strong shock (blast) wave in a van der Waals gas and small solid particles mixture. The small solid particles are continuously distributed in the mixture and the equilibrium conditions for flow are maintained. To derive the analytical solutions, the physical variables such as density, pressure, and velocity are expanded using perturbation method in power series. The solutions are derived in analytical form for first approximation, and for second order approximation the set of differential equations are also obtained. The effects of an increase in the problem parameters value on the physical variables are investigated for first order approximation. A comparison is also, made between the solution of cylindrical shock and spherical shock. It is found that the fluid density and fluid pressure become zero near the point or axis of symmetry in spherical or cylindrical symmetry, respectively, and therefore a vacuum is created near the point or axis of symmetry which is in tremendous conformity with the physical condition in laboratory to generate the shock wave.

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.

scholarly journals Relating mass movement with electrical self-potential signals

2018 ◽  
Vol 216 (1) ◽  
pp. 55-60 ◽  
Author(s):  
T Heinze ◽  
JK Limbrock ◽  
SP Pudasaini ◽  
A Kemna
Keyword(s):  
Mass Movement ◽  
Fluid Pressure ◽  
Streaming Potential ◽  
Electric Signal ◽  
Hydraulic Pressure ◽  
Partially Saturated ◽  
Internal Surfaces ◽  
Partially Saturated Soil ◽  
Electrically Charged ◽  
Self Potential

SUMMARY Landslides present a latent danger to lives and infrastructure worldwide. Often such mass movements are caused by increasing pore pressure. The electrical self-potential (SP) method has been applied in a broad range of monitoring studies. When fluid flow is involved the most relevant source of SP is the streaming potential, caused by the flow of an electrolyte through porous media with electrically charged internal surfaces. We experimentally investigated the SP signal associated with deformation of partially saturated soil. For partly saturated scenarios, we observed an SP signature correlated with the mass movement. In dry experiments, we did not observe any significant change in the electric signal. Results of numerical simulations match with the experimental observations when assuming a local and temporary alteration of the hydraulic pressure due to the sliding mass. Our findings suggest that SP measurements can be used to observe mass movement triggered by fluid pressure variations through the streaming potential.

Sign in / Sign up

Export Citation Format

Share Document