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Conservation equations for mass, momentum, energy, and entropy are formulated for the phases and interfaces of a three‐phase system consisting of a solid and two immiscible fluids. The microscale equations are averaged to the macroscale by integration over a representative elementary volume. Thermodynamic statements for each of the phases and interface entities are also formulated at the microscale and then averaged to the macroscale. This departure from most uses of thermodynamics in macroscale analysis ensures consistency between models and parameters at the two scales. The expressions for the macroscale rates of change of internal energy are obtained by differentiating the derived forms for energy and making use of averaging theorems. These thermodynamic expressions, along with the conservation equations, serve as constraints on the entropy inequality. A linearization of the resulting equations is employed to investigate the theoretical origins of the Biot coefficient that relates the hydrostatic part of the total stress tensor to the normal force applied at the solid surface by the pore fluids. The results here are placed in the context of other formulations and expressions that appear in the literature. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
94.
Characterization of a reservoir model requires determination of its petrophysical parameters, such as porosity and saturation.
We propose a new method to determine these parameters directly from seismic data. The method consists of the computation and
inversion of seismic waveforms. A high frequency method is presented to model wave propagation through an attenuative and
dispersive poroelastic medium. The high frequency approximation makes it possible to efficiently compute sensitivity functions.
This enables the inversion of seismic waveforms for porosity and saturation. The waveform inversion algorithm is applied to
two laboratory crosswell datasets of a water saturated sand. The starting models were obtained using travel time tomography.
The first dataset is inverted for porosity. The misfit reduction for this dataset is approximately 50%. The second dataset
was obtained after injection of a nonaqueous-phase liquid (NAPL), possibly with some air, which made the medium more heterogeneous.
This dataset was inverted for NAPL and air saturation using the porosity model obtained from the first inversion. The misfit
reduction of the second experiment was 70%. Regions of high NAPL and high air saturation were found at the same location.
These areas correlate well with the position of one of the injection points as well as regions of higher NAPL concentrations
found after excavation of the sand. It is therefore possible to directly invert waveforms for pore fluid saturation by taking
into account the attenuation and dispersion caused by the poroelasticity. 相似文献
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A new anisotropic poroelastic damage model is proposed for saturated brittle porous materials. The model is formulated in the framework of the continuum damage mechanics. A second‐rank symmetric tensor is used to characterize material damage due to oriented microcracks. The classic Biot poroelastic theory is then extended to include poroelastic damage coupling. Both the deterioration of elastic properties and poroelastic coefficients is taken into account. A suitable procedure for determination of model parameters from standard laboratory tests is presented. The validity of the model is tested through comparison between numerical predictions and experimental data in various loading conditions. The overall performance of the model is evaluated. The choice of relevant effective stress for the microcrack propagation criterion in saturated cohesive geomaterials is discussed. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
97.
A dual-porosity poroelastic model is extended to represent behaviour in cylindrical co-ordinates for the evaluation of flow-deformation effects in cylindrical laboratory samples incorporating a central wellbore or non-repeating axisymmetric injection on the periphery. Nine-node quadratic elements are used to represent mechanical deformation, while eight-node linear elements are used to interpolate the pressure fields, which offers significant advantages over the behaviour of other non-conforming elements. The model presented is validated against simplified analytical results, and extended to describe the behaviour of homogeneous and heterogeneous laboratory specimens subjected to controlled triaxial state of stress and injection tests. Apparent from the results is the significant influence of stress-deformation effects over system behaviour. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
98.
Existing solutions to Mandel's problem focus on isotropic, transversely isotropic, and orthotropic materials, the last two of which have one of the material symmetry axes coincide with the vertical loading direction. The classical plane strain condition holds for all these cases. In this work, analytical solution to Mandel's problem with the most general matrix anisotropy is presented. This newly derived analytical solution for fully anisotropic materials has all the three nonzero shear strains. Warping occurs in the cross sections, and a generalized plane strain condition is fulfilled. This solution can be applied to transversely isotropic and orthotropic materials whose material symmetry axes are not aligned with the vertical loading direction. It is the first analytical poroelastic solution considering mechanical general anisotropy of elasticity. The solution captures the effects of material anisotropy and the deviation of the material symmetry axes from the vertical loading direction on the responses of pore pressure, stress, strain, and displacement. It can be used to match, calibrate, and simulate experimental results to estimate anisotropic poromechanical parameters. This generalized solution is capable of reproducing the existing solutions as special cases. As an application, the solution is used to study the responses of transversely isotropic and orthotropic materials whose symmetry axes are not aligned with the vertical loading direction. Examples on anisotropic shale rocks show that the effects of material anisotropy are significant. Mandel-Cryer's effects are highly impacted by the degree of material anisotropy and the deviation of the material symmetry axes from the vertical loading direction. 相似文献
99.
The method of fundamental solution for 3‐D wave scattering in a fluid‐saturated poroelastic infinite domain 
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下载免费PDF全文 Zhongxian Liu Zhikun Wang Alexander H.D. Cheng Jianwen Liang Chuchu Wang 《国际地质力学数值与分析法杂志》2018,42(15):1866-1889
By using a complete set of poroelastodynamic spherical wave potentials (SWPs) representing a fast compressional wave PI, a slow compressional wave PII, and a shear wave S with 3 vectorial potentials (not all are independent), a solution scheme based on the method of fundamental solution (MFS) is devised to solve 3‐D wave scattering and dynamic stress concentration problems due to inhomogeneous inclusions and cavities embedded in an infinite poroelastic domain. The method is verified by comparing the result with the elastic analytical solution, which is a degenerated case, as well as with poroelastic solution obtained using other numerical methods. The accuracy and stability of the SWP‐MFS are also demonstrated. The displacement, hoop stress, and fluid pore pressure around spherical cavity and poroelastic inclusion with permeable and impermeable boundary are investigated for incident plane PI and SV waves. The scattering characteristics are examined for a range of material properties, such as porosity and shear modulus contrast, over a range of frequency. Compared with other boundary‐based numerical strategy, such as the boundary element method and the indirect boundary integral equation method, the current SWP‐MFS is a meshless method that does not need elements to approximate the geometry and is free from the treatment of singularities. The SWP‐MFS is a highly accurate and efficient solution methodology for wave scattering problems of arbitrary geometry, particularly when a part of the domain extends to infinity. 相似文献
100.
Fushen Liu 《国际地质力学数值与分析法杂志》2020,44(12):1634-1655
The paper presents an embedded strong discontinuity approach to simulate single hydraulic fracture propagation in the poroelastic medium under plane-strain conditions. The method enriches the strain field with the discontinuous deformation mode and allows the fracture to be modeled inside elements. The Mode-I fracture initiation and propagation are described by the trilinear cohesive law, which is implemented by the penalty method. The enhanced permeability inside the fractured elements is dependent on the fracture aperture. Hydraulic fracture propagation is driven by the high pressure gradient near the fracture. Fluid transfer between the fracture and bulk rock is automatically captured within the poroelastic framework. The numerical framework is verified by the comparisons with the asymptotic analytical solutions for single hydraulic fracture propagation. 相似文献