ONSET CONDITION OF STRAIN LOCALIZATION IN MATRIX OF SATURATED POROUS MEDIA

Based on governing equations of saturated porous media and Liapunov＇ s stability here, onset conditions matrix of porous media used by solid stress and Terzaghi＇s effective stress constitutive description under seepage flow state, are presented, which have different forms with different representation of the solid phase, matrix or skeleton, constitutive model of porous media. The main difference relates with how to describe the interaction between solid phase and liquid phase in constitutive model. The derived onset condition of strain localization under Terzaghi＇ s effective stress description can be used to interpret different failure types, piping effect, landslides and mudflows, by means of the type and the magnitude ratio of relative movement between solid phase and liquid phase. Examples here illuminate the onset condition of how to work.

Effective stress law for anisotropic double porous media

An effective stress law is derived analytically to describe the effect of pore (fracture pore and matrix-block pore) fluid pressure on the linearly elastic response of ani- sotropic saturated dual-porous rocks, which exhibit anisot- ropy. For general anisotropy the difference between the ef- fective stress and the applied stress is not hydrostatic simply multiplied by Biot coefficient. The effective stress law in- volves four constants for transversely isotropic response; these constants can be expressed in terms of the moduli of the single porous material, double porous material and of the solid material. These expressions are simplified considerably when the anisotropy is structural rather than intrinsic, i.e. in the case of an isotropic solid material with an anisotropic pore structure. In this case the effective stress law involves grain bulk modulus, four moduli and two compliances of the porous material for transverse isotropy. The law reduces, in the case of isotropic response, to that suggested by Li Shuiquan (2001). And reduction to the single-porosity (de- rived analytically by Carroll (1979)) is presented to demon- strate the conceptual consistency of the proposed law.

ACOUSTOELASTIC THEORY FOR FLUID-SATURATED POROUS MEDIA

Based on the finite deformation theory of the continuum and poroelastic theory, the aeoustoelastic theory for fluid-saturated porous media （FSPM） in natural and initial coordi- nates is developed to investigate the influence of effective stresses and fluid pore pressure on wave velocities. Firstly, the assumption of a small dynamic motion superimposed on a largely static pre- deformation of the FSPM yields natural, initial, and final configurations, whose displacements, strains, and stresses of the solid-skeleton and the fluid in an FSPM particle could be described in natural and initial coordinates, respectively. Secondly, the subtraction of initial-state equations of equilibrium from the final-state equations of motion and the introduction of non-linear constitu- rive relations of the FSPM lead to equations of motion for the small dynamic motion. Thirdly, the consideration of homogeneous pre-deformation and the plane harmonic form of the small dynamic motion gives an acoustoelastic equation, which provides analytical formulations for the relation of the fast longitudinal wave, the fast shear wave, the slow shear wave, and the slow longitudinal wave with solid-skeleton stresses and fluid pore-pressure. Lastly, an isotropic FSPM under the close-pore jacketed condition, open-pore jacketed condition, traditional unjacketed condition, and triaxial condition is taken as an example to discuss the velocities of the fast and slow shear waves propagating along the direction of one of the initial principal solid-skeleton strains. The detailed discussion shows that the wave velocities of the FSPM are usually influenced by the effective stresses and the fluid pore pressure. The fluid pore-pressure has little effect on the wave velocities of the FSPM only when the components of the applied initial principal solid-skeleton stresses or strains are equal, which is consistent with the previous experimental results.

Rheology of a Viscous-Plastic Liquid in a Porous Medium

The hydrodynamics of the capillary flow of a viscous-plastic liquid in cylindrical rectilinear pores is considered, as a result of which the structural velocity distribution over the pore cross section is obtained. Analytical solutions are proposed for the equations of hydraulic diffusion and nonlinear filtration for a non-Newtonian fluid in a cylindrical porous medium. It is noted that when a non-Newtonian fluid flows in a porous medium, the filtration equations take a nonlinear form due to the effective viscosity, shear, and yield stresses taken into account in its structure. The proposed solutions make it possible to evaluate the state of the porous medium and its main parameters (permeability, hydraulic diffusion, and effective viscosity coefficients). The obtained solutions are compared with existing experimental data for non-Newtonian oils.

Confinement effect on CO_(2)and CH_(4)permeability in shale

Gas flow in shales follows a number of physical mechanisms that include Knudsen diffusion,Darcy flow,and adsorption in the matrix and micro pores.The aim of the study is to resolve the interplay of gas transport in these media at increased effective stress as well as net pore pressure.In this research,we investigated the nature of gas transport in the matrix of shale by sending He,CH_(4)and CO_(2)gases through a transient upstream pressure pulse decay instrument.A series of experiments were conducted at constant pore pressures and a gradually increasing confining pressure.The same study was done in three different scenarios,injecting He,CO_(2)and CH_(4).At a constant pore pressure,gas permeability appears to decrease with an increasing confining pressure and effective stress.With increasing effective stress,the slip factor also decreases along with the permeability.The decrease in slip could be attributed to prestressing,that is likely to create new fractures.Among the three purged gases,permeability of shale to CH_(4)is the highest,and that to CO_(2)is the lowest owing to its high adsorption.Higher permeability of CH_(4)against He,could be attributed to the dual transport mechanism.

Stress dependence of elastic wave dispersion and attenuation in fluid-saturated porous layered media

The fluid-saturated porous layered(FSPL)media widely exist in the Earth's subsurface and their overall mechanical properties,microscopic pore structure and wave propagation characteristics are highly relevant to the in-situ stress.However,the effect of in-situ stress on wave propagation in FSPL media cannot be well explained with the existing theories.To fill this gap,we propose the dynamic equations for FSPL media under the effect of in-situ stress based on the theories of poroacoustoelasticity and anisotropic elasticity.Biot loss mechanism is considered to account for the stress-dependent wave dispersion and attenuation induced by global wave-induced fluid flow.Thomsen's elastic anisotropy parameters are used to represent the anisotropy of the skeleton.A plane-wave analysis is implemented on dynamic equations yields the analytic solutions for fast and slow P waves and two S waves.Modelling results show that the elastic anisotropy parameters significantly determine the stress dependence of wave velocities.Vertical tortuosity and permeability have remarkable effects on fast and slow P-wave velocity curves and the corresponding attenuation peaks but have little effect on S-wave velocity.The difference in velocities of two S waves occurs when the FSPL medium is subjected to horizontal uniaxial stress,and the S wave along the stress direction has a larger velocity,which implies that the additional anisotropy other than that induced by the beddings appears due to horizontal stress.Besides,the predicted velocity results have the reasonable agreement with laboratory measurements.Our equations and results are relevant to a better understanding of wave propagation in deep strata,which provide some new theoretical insights in the rock physics,hydrocarbon exploration and stress detection in deep-strata shale reservoirs.

地下各种压力之间关系式的修正

目前在钻井工程中普遍采用的地下各种压力之间的关系式是不严格的。研究把岩石视为多孔介质,从多孔介质的角度出发,重新建立上覆岩层压力、孔隙流体压力、基岩应力之间的关系式,该式包含了岩石作为多孔介质的一个重要参数孔隙度F。

多孔介质的双重有效应力

多孔介质存在两种变形机制,本体变形和结构变形;与此相对应、多孔介质也具有两个有效应力、本体有效应力和结构有效应力;本体有效应力决定多孔介质的本体变形、结构有效应力决定多孔介质的结构变形;多孔介质具有双重有效应力,这是由介质独特的物质结构所决定的固有特性.

基于分形方法的多孔介质有效应力模型研究

在充分分析国内外多孔介质有效应力研究基础上,针对石油工程中深层岩石复杂结构特征,应用分形几何理论,分别建立了深层多孔介质岩石有效应力的二维和三维分形计算模型。该模型能反应任意孔隙结构下的应力作用关系,是现有相关有效应力模型的补充和完善。为了现场应用方便,进一步给出多孔介质有效应力分形模型的简化式。实例计算表明,应用简化式计算的有效应力值误差在7%以内,可以满足油田现场的要求,并且应用简化式有利于应用测井数据获得连续的有效应力剖面。

饱和多孔介质流固耦合渗流的数学模型

将基于多孔介质的有效应力原理引入流固耦合渗流中 ,并根据平衡条件得出了应力场方程 ;充分分析流固耦合渗流的物理特性 ,建立起孔隙度和渗透率动态模型 ;依据流体力学连续性方程 ,考虑流固耦合情形下多孔介质骨架变形特性和流体的可压缩性 ,得到了孔隙流体的连续性方程 ,即渗流场方程。在以上诸方程的基础上辅助以定解条件 ,建立起了完备的饱和多孔介质流固耦合渗流的数学模型。本文还对模型进行了简化分析 ,并与经典一维固结理论作定性对比 ,分析表明 ,经典的固结理论可认为是本文模型的一种简化。

多孔介质应力关系方程

Ｔｅｒｚａｇｈｉ方程（σ＝σＧ＋Ｐ）是描述多孔介质应力关系的经典方程，由于方程同时定义了二个不可测量，因而是不实用的；方程没有引入反映多孔介质特性的最重要参数（φ），因而是不妥当的；鉴于方程存在的问题，本文对其进行了深入的研究，重新建立了多孔介质应力之间的关系方程：σ＝φＰ＋（１－φ）σＧ；由于φ的引入，新方程更全面、更合理地反映了多孔介质固有的力学特性．

Theoretical analysis of influencing factors on resistance in the process of gas migration in coal seams

Inspired by previous resistance models for porous media, a resistance expression of gas migration within coal seams based on the ideal matchstick geometry, combined with the Darcy equation and the modified Poiseuille equation is proposed. The resistance to gas migration is generally dynamic because of the variations in adsorption swelling and matrix shrinkage. Due to the limitations of experimental conditions,only a theoretical expression of resistance to gas migration in coal is deduced, and the impacts of tortuosity, effective stress and pore pressure on the resistance are then considered. To validate the proposed expression, previous data from other researchers are adopted for the history matching exercise, and the agreement between the two is good.

Revisiting the methods of determining hydraulic conductivity of saturated expansive clays in low-compressibility zone

The hydraulic conductivity of saturated clays is commonly determined either directly by monitoring water flux or indirectly based on Terzaghi’s consolidation equation.Similar results are generally obtained from the two methods,but sometimes a significant difference can be observed,in particular for expansive soils.In this study,the hydraulic conductivities determined by the two methods are first compared based on existing data in the literature.The indirect method is then revisited attempting to explain the difference identified.A modified effective stress,considering physico-chemical interaction between face-to-face oriented particles,is finally introduced to better describe the compressibility of expansive clays and to further improve the indirect method in determining hydraulic conductivity of such soils in the low-compressibility zone.Extra tests were performed on Gaomiaozi(GMZ)bentonite slurry and the results obtained allowed the modified indirect method to be verified.

围压-孔压改变条件下致密砂岩及泥页岩泊松比变化特征及机制

在围压(外压)或孔压(内压)发生变化的条件下,致密砂岩及泥页岩泊松比的变化特征及机制仍有待厘清。本研究从Terzaghi有效应力理论和国内学者提出的新有效应力概念出发,基于松辽盆地高台子组致密砂岩、青山口组泥页岩三向动、静态泊松比测定结果,剖析了两类岩石泊松比的变化特征及机制。岩石样品三向泊松比变化曲线的分布呈现显著的各向异性,这将对压裂缝的延展规律产生一定的影响;就“有效应力”概念厘定的科学性而言,“Terzaghi有效应力”适用于裂缝较为发育的储层,而“新有效应力”适用于孔隙度较大且分布较为均匀的泥页岩。结论将为致密油气的有效开发提供较为重要的理论依据。

再谈双重有效应力——对《双重有效应力再认识及其综合作用》一文的讨论与分析

有效应力是多孔介质力学的基础概念,固体力学的理论通过有效应力应用于多孔介质,产生了多孔介质力学。但是,不同学者在不同条件下提出的有效应力有所不同,这就给有效应力的应用带来了不确定性。目前已提出了3个典型的有效应力:Terzaghi有效应力、Biot有效应力和双重有效应力。Terzaghi有效应力是针对疏松土介质提出的第一个有效应力,催生了土力学的诞生,它仅适用于极其疏松的多孔介质,不适用于致密介质的力学行为研究。Biot有效应力是对Terzaghi有效应力的修正,由于Biot系数没有明确的物理意义,又通常取经验值,因此Biot有效应力公式是一个经验公式。双重有效应力是在介质变形机制基础上提出的有效应力概念。多孔介质存在两种基本的变形机制:本体变形和结构变形。与此相对应,多孔介质存在两个有效应力:本体有效应力和结构有效应力。本体有效应力决定多孔介质的本体变形,结构有效应力决定多孔介质的结构变形。双重有效应力考虑了多孔介质的物质结构,引入了多孔介质的物性参数,参数取不同的数值,可用于不同的介质类型。毛博士提出的新双重有效应力概念定义不严谨,科学性不强,无法通过实践检验。多孔介质的孔隙压缩系数与孔隙度不是负相关,而是正相关。

Derivation of the work expression and discussion on the effective principle and the phase separation theorem in unsaturated soil

Based on the balance equations for mass, linear momentum, energy in porous media theory and some hypotheses in unsaturated soil mechanics, an expression of the total deformation work W is derived, and with the help of the specific ex-pression of the work, the effective stress conjugated with the displacement of the soil skeleton is suggested by the authors, which has the similar form as the expressions proposed by Wheeler (2003) and some other researchers according to their experience and intuition, but the effective stress presented in this paper is derived on the basis of porous media theory and its assumptions, whose premise and hypothesis are clear. It is also pointed out that due to the complexity of the physical mechanism and various influencing factors, it is impossible in unsatu-rated soil mechanics to determine the deformation of solid skeleton by the effective stress only, like in the saturated soil mechanics. Besides, by using the expression of the deformation work and the free energy Aα for each phase, the applicability of the Phase Separation Principle proposed by Passman (1984) in unsaturated soil is discussed, and it is considered that the principle should not strictly apply to un-saturated soil mechanics.