Wyniki wyszukiwania - BazTech

1

Application of the thermoporoelasticity model in numerical modelling of underground coal gasification influence on the surrounding medium

Uciechowska-Grakowicz Anna, Strzelecki Tomasz

Studia Geotechnica et Mechanica

|

2021

|

Vol. 43, nr 2

116--134

EN

The purpose of this paper was to present the thermoporoelasticity model adapted for application in modelling processes, where phase transition may occur, such as during underground coal gasification (UCG). The mathematical model of the medium (soil/rock with pores filled with liquid/gas) in non-isothermal conditions is based on Biot’s poroelasticity model. The poroelasticity model is expanded here by the influence of temperature and adjusted to the case where both liquid and highly compressible fluid are present in pores by using the gas laws. This requires considering temperature-dependent physical quantities such as pore fluid density, heat transfer coefficient and viscosity as functions of temperature. Based on the proposed mathematical model and the finite element method, a numerical model was built for the purpose of computing processes occurring in the vicinity of the UCG generator. The result of the authors’ work is a three-dimensional (3D) model, which was not only modified, but derived straight from the laws of thermodynamics, where fields of displacement, temperature and fluid flow are coupled. The model makes it possible to determine results significant to modelling of the UCG process, the reach of the gaseous phase’s presence in pores, subsidence values, temperature distribution and directions and rate of seepage, without losing the simplicity and elegance of Biot’s original concept. Next, the results of simulations for a hypothetical deposit to estimate the environmental impact of UCG are presented. After applying specific geometry and parameters, the model can be useful for verifying if the chosen technology of UCG in specific conditions will be safe for the environment and infrastructure.

2

About some problems related to determination of the e.g. Biot coefficient for rocks

Nowakowski Andrzej, Nurkowski Janusz

Archives of Mining Sciences

|

2021

|

Vol. 66, no. 1

133--150

EN

Use of the poroelasticity theory by Biot in the description of rock behaviour requires the value of the e.g. Biot coefficient α to be determined. The α coefficient is a function of two moduli of compressibility: the modulus of compressibility of the rock skeleton Ks and the effective modulus of compressibility K. These moduli are determined directly on the basis of rock compressibility curves obtained during compression of a rock sample using hydrostatic pressure. There is also a concept suggesting that these compressibility moduli might be determined on the basis of results of the uniaxial compression test using the fact that, in the case of an elastic, homogeneous and isotropic material, the modulus of compressibility of a material is a function of its Young modulus and its Poisson ratio. This work compares the results obtained from determination of the Biot coefficient by means of results of compressibility test and uniaxial compression test. It was shown that the uniaxial compression test results are generally unsuitable to determine the value of the coefficient α. An analysis of values of the determined moduli of compressibility shows that whereas the values of effective moduli of compressibility obtained using both ways may be considered as satisfactorily comparable, values of the relevant rock skeleton moduli of compressibility differ significantly.

3

Simulation of seismic wave propagation in poroelastic media using vectorized Biot’s equations: an application to a CO2 sequestration monitoring case

Anthony Emmanuel, Vedanti Nimisha

Acta Geophysica

|

2020

|

Vol. 68, no. 2

435--444

EN

Wave propagation through porous media allows us to understand the response and interaction that occur between the elastic rock matrix and the fuid. This interaction has been described by Biot in his theory of poroelasticity. Seismic wave simulation using Biot’s formulations is computationally expensive when compared with the acoustic and elastic cases. This computational burden can be reduced by reformulating the numerical derivative operators to improve the efciency. To achieve this, we used a staggered-grid fnite diference operator to discretize 2D velocity stress equations as given by Biot’s theory. A vectorized derivative is applied on the staggered grid by shifting the coordinates. The reformulated equations were applied to compute the seismic response of a reservoir, where CO2 is being injected and the efect of injected CO2 in the formation is clearly seen in the synthetic data generated. The algorithm was coded in Python and to test its efciency, the simulation run-time was compared for both serial and vectorized equations, and the speed-up ratio was calculated. Our results show a decrease in the simulation run-time for the vectorized execution with over a factor of a hundred percent (100%). We further observed that the amplitudes of the events increase with an increase in CO2 saturation in the formation. This matches well with the real data.

4

Numerical model of heat transfer in three phases of the poroelastic medium

Uciechowska-Grakowicz A., Strzelecki T.

Studia Geotechnica et Mechanica

|

2016

|

Vol. 38, nr 2

53—59

EN

In this paper, the results of numerical analysis of the thermal consolidation of a two phase medium, under the assumption of independent heat transfer in fluid and the solid phase of the medium, are presented. Three cases of pore fluid were considered: liquid, represented by water, and gas, represented by air and carbon dioxide. The mathematical model was derived from irreversible thermodynamics, with the assumption of a constant heat transfer between the phases. In the case of the accepted geometry of the classical dimensions of the soil sample and boundary conditions, the process leads to equalization of temperatures of the skeleton on the pore fluid. Heat transfer is associated with the fluid flow in the pores of the medium. In the case of gas as the pore fluid, a non-linear mathematical model of gas filtration through the pores of the medium was accepted. For the computing process, relationships between viscosity or density and temperature proposed by other authors were taken into account. Despite accepting mechanical constants of the solid phase that do not depend on temperature, the obtained model is nonlinear and develops the classical Biot–Darcy model.

5

Effects of the microcrack shape, size and direction on the poroelastic behaviors of a single osteon: a finite element study

Cen H-P., Wu X-G., Yu W-L., Liu Q-Z., Yia Y-M.

Acta of Bioengineering and Biomechanics

|

2016

|

Vol. 18, no. 1

3--10

EN

In this work, a finite element study is proposed by using the Comsol Multiphysics software to evaluate the effects of microcrack shape, size and direction on the poroelastic behaviors of a single osteon. Methods: This finite element model is established by using the Comsol Multiphysics software, and we just focus on the comparison of the influences of those microcrack geometric parameters on the osteonal fluid pressure and velocity. Results: The results show that: (1) microcracks in the osteon wall can induce a release of the fluid pressure, but enlarge the velocity in this region; (2) equal-area microcrack with ellipsoid-like shape produced a larger fluid pressure and velocity fields in the osteon than that of rectangular shape; (3) in the elliptic microcracks, the longer of the length (major semi-axis) induces a smaller fluid pressure and velocity amplitudes, whereas the width (minor axis) has little effect; (4) the direction of the microcracks (major axial direction) has an limited influence area around about 1/15 of the osteon cross-sectional area. Conclusions: This model permits the linking of the external loads and microcracks to the osteonal fluid pressure and velocity, which can be used for other purpose associate microcracks with the mechanotransduction and bone remodeling.

6

Skinfold creep under load of caliper. Linear visco- and poroelastic model simulations

Nowak J., Nowak B., Kaczmarek M.

Acta of Bioengineering and Biomechanics

|

2015

|

Vol. 17, no. 4

39--48

EN

Purpose: This paper addresses the diagnostic idea proposed in [11] to measure the parameter called rate of creep of axillary fold of tissue using modified Harpenden skinfold caliper in order to distinguish normal and edematous tissue. Our simulations are intended to help understanding the creep phenomenon and creep rate parameter as a sensitive indicator of edema existence. The parametric analysis shows the tissue behavior under the external load as well as its sensitivity to changes of crucial hydro-mechanical tissue parameters, e.g., permeability or stiffness. Methods: The linear viscoelastic and poroelastic models of normal (single phase) and oedematous tissue (twophase: swelled tissue with excess of interstitial fluid) implemented in COMSOL Multiphysics environment are used. Simulations are performed within the range of small strains for a simplified fold geometry, material characterization and boundary conditions. The predicted creep is the result of viscosity (viscoelastic model) or pore fluid displacement (poroelastic model) in tissue. Results: The tissue deformations, interstitial fluid pressure as well as interstitial fluid velocity are discussed in parametric analysis with respect to elasticity modulus, relaxation time or permeability of tissue. The creep rate determined within the models of tissue is compared and referred to the diagnostic idea in [11]. Conclusions: The results obtained from the two linear models of subcutaneous tissue indicate that the form of creep curve and the creep rate are sensitive to material parameters which characterize the tissue. However, the adopted modelling assumptions point to a limited applicability of the creep rate as the discriminant of oedema.

7

Fundamentals of multiphysics modelling of piezo-poro-elastic structures

Zieliński T. G.

Archives of Mechanics

|

2010

|

Vol. 62, nr 5

343-378

EN

The paper discusses theoretical fundamentals necessary for accurate vibroacoustical modeling of structures or composites made up of poroelastic, elastic, and (active) piezoelectric materials, immersed in an acoustic medium (e.g. air). An accuratemodeling of such hybrid active-passive vibroacoustic attenuators (absorbers or insulators) requires a multiphysics approach involving the finite element method to cope with complex geometries. Such fully-coupled, multiphysics model is given in this paper. To this end, first, the accurate PDE-based models of all the involved single-physics problems are recalled and, since a mutual interaction of these various problems is of the uttermost importance, the relevant couplings are thoroughly investigated and taken into account in the modeling. Eventually, the Galerkin finite element model is developed. This model should serve to develop designs of active composite vibroacoustic attenuators made up of porous foams with passive and active solid implants, or hybrid liners and panels made up of a core or layers of porous materials fixed to elastic faceplates with piezoelectric actuators, and coupled to air-gaps. A widespread design of such smart mufflers is still an open topic and should be addressed with accurate predictive tools based on the model proposed in the present paper. The model is accurate in the framework of kinematical and constitutive (material) linearity of behaviour. This is, however, the very case of the vibroacoustic application of elasto-poroelastic panels or composites, where the structural vibrations are induced by acoustic waves. The developed fully-coupled FE model is finally used to solve a generic two-dimensional example and some issues concerning finite element approximation and convergence are also discussed.

8

Fabric dependence of bone ultrasound

Cowin S. C., Cardoso L.

Acta of Bioengineering and Biomechanics

|

2010

|

Vol. 12, no. 2

3-23

EN

Current diagnosis of bone loss and osteoporosis is based on the measurement of the Bone Mineral Density (BMD) or the apparent mass density. Unfortunately, in most clinical ultrasound densitometers: 1) measurements are often performed in a single anatomical direction, 2) only the first wave arriving to the ultrasound probe is characterized, and 3) the analysis of bone status is based on empirical relationships between measurable quantities such as Speed of Sound (SOS) and Broadband Ultrasound Attenuation (BUA) and the density of the porous medium. However, the existence of a second wave in cancellous bone has been reported, which is an unequivocal signature of poroelastic media, as predicted by Biot’s poroelastic wave propagation theory. A fabric-dependent anisotropic poroelastic approach is empolyed as a theoretical framework to describe the microarchitectural-dependent relationship between measurable wave properties and the elastic constants of trabecular bone, and thus represents an alternative for bone quality assessment beyond BMD alone.

9

Surface waves in a heterogeneous layer over a liquid saturated poro-elastic solid half space

Pal P.

Acta Geophysica Polonica

|

2000

|

Vol. 48, nr 2

195-205

EN

Rayleigh waves in a heterogeneous layer over a saturated half space are investigated under plane strain conditions. The dispersion equation is derived using the methods for propagation of free waves in layered media. The effect of heterogeneity on phase velocity is studied by taking different numerical values of heterogeneity factor and the result is shown graphically.