含孔隙、裂隙地层随钻多极子声波测井理论

储层岩石中普遍存在孔隙与裂隙,对钻井中的测井声波产生重要影响.基于孔、裂隙介质弹性波理论,导出了随钻声波测井的井孔声场表达式.据此考察了地层裂隙密度与含气饱和度的变化时井孔内随钻多极子模式波（斯通利波、弯曲波和螺旋波）的速度、衰减与灵敏度以及地层纵、横波的响应特征.裂隙密度与含气饱和度对模式波的速度频散与衰减都有影响,且两参数的值越大,影响越大.具体来说,速度对裂隙密度更敏感,而衰减对含气饱和度更敏感.具有"艾里相"特征的随钻偶极和四极子波在地层含气时产生强烈衰减,可以作为判断地层含气的一个明显指示.理论模拟与实际测井数据分析结果符合较好.     

Upscaling relative permeabilities in a structured porous medium

Upscaling of multi-phase flow problems for a heterogeneous porous medium requires modification of constitutive functions at the grid-block scale. A particular type of heterogeneity that has important environmental consequences involves thin, continuous streaks of high permeability through lower-permeability background rocks. These streaks, which may correspond to features like abandoned wells in mature sedimentary basins, can become preferential flow paths for an invading fluid. Quantification of flow through these types of heterogeneities in deep, geological formations is necessary for estimates of migration and possible leakage of injected fluids such as hazardous liquid wastes, municipal liquid wastes, and, possibly, carbon dioxide. One of the important constitutive functions for proper estimation of flow through these flow paths is the relative permeability function. In the simple case of a single high-permeability streak in a uniform rock matrix, with both materials having identical (local) relative permeability functions, the upscaled relative permeability must be changed significantly to capture the proper leakage. Standard petroleum reservoir pseudo-functions for relative permeability capture the general features of the upscaled function, but they still produce errors of several hundred percent in the leakage estimation. Detailed three-dimensional numerical simulations and associated upscaled calculations demonstrate the proper form for the upscaled relative permeability, and provide a modified derivation of pseudo-functions to capture the leakage behavior in upscaled models.     

Penetrative convection and multi-component diffusion in a porous medium

Linear instability and nonlinear energy stability analyses are developed for the problem of a fluid-saturated porous layer stratified by penetrative thermal convection and two salt concentrations. Unusual neutral curves are obtained, in particular non-perfect `heart-shaped' oscillatory curves that are disconnected from the stationary neutral curve. These curves show that three critical values of the thermal Rayleigh number may be required to fully describe the linear stability criteria. As the penetrative effect is increased, the oscillatory curves depart more and more from a perfect heart shape. For certain values of the parameters it is shown that the minima on the oscillatory and stationary curves occur at the same Rayleigh number but different wavenumbers, offering the prospect of different types of instability occurring simultaneously at different wavenumbers. A weighted energy method is used to investigate the nonlinear stability of the problem and yields unconditional results guaranteeing nonlinear stability for initial perturbations of arbitrary sized amplitude.     

Acoustic reflection logging for open and cased holes

In the present work, the waveforms of reflected wave sonic log for open and cased boreholes are calculated. Calculations are performed for a borehole containing an acoustic multipole source (monopole, dipole, or quadrupole). A reflected wave is more efficiently excited at resonant frequencies. These frequencies for all source types are close to the frequencies of oscillations of a fluid column located in an absolutely rigid hollow cylinder. It is shown that the acoustic reverberation is controlled by the acoustic impedance of the rock Z = V_p ρ_s for fixed parameters of the borehole fluid, where V_p is the compressional wave velocity in the rock, and ρ_s is the rock density. This result is correct for all types of acoustic sources (monopole, dipole, or quadrupole). Methods of the waveform processing for determining parameters characterizing the reflected wave are discussed.     

声波测井相控圆弧阵及其辐射指向性

为了实现声波测井的周向分辨能力,提出了可应用于声波测井的、具有周向辐射指向性的相控圆弧阵声波辐射器方案.声波测井圆弧阵发射换能器由多个压电振子沿着圆周排列,通过控制各个振子的激励时间可以实现向某个方位方向的声波辐射.本文以自制的28阵元相控圆弧阵为例,理论和实验研究了相控圆弧阵的辐射指向性及其与阵元个数、声波频率等参数之间的关系.研究表明,在声波测井频率范围内,随着工作阵元个数和频率的增加,圆弧阵辐射声波的周向指向性增强,理论研究和实验研究取得了相一致的结果.与现有的声波测井单极子、偶极子和四极子声源相比,在井下采用相控圆弧阵作为声波辐射器可以真正实现方位声波测井,在各向异性地层评价、定向钻井和井间地层评价等石油工程中有良好的应用前景.     

Simulating a lake as a high-conductivity variably saturated porous medium

One approach for simulating ground water–lake interactions is to incorporate the lake into the ground water solution domain as a high-conductivity region. Previous studies have developed this approach using fully saturated models. This study extends this approach to variably saturated models, so that ground water–lake interactions may be more easily simulated with commonly used or public domain variably saturated codes that do not explicitly support coupled lake–water balance modeling. General guidelines are developed for the choices of saturated hydraulic conductivity and moisture retention and relative permeability curves for the lake region. When applied to an example ground water–lake system, model results are very similar to those from a model in which the lake is represented as a specified head boundary continuously updated by a lake mass balance. The high-conductivity region approach is most suitable for relatively simple geometries and lakes with slower and smaller fluctuations when the overall flow pattern and system fluxes, rather than the detailed flow pattern around the intersection of the lake and land surfaces, are of interest.     

Heat dispersion effect on thermal convection in a porous medium layer

Thermal convection resulting from vertical temperature gradients in porous media is analyzed. The effect of heat dispersion is taken into account. It is found that heat dispersion increases the thermal stability of the flow field and may inhibit the appearance of convection currents, which would appear if dispersion effects are omitted.The longitudinal as well as the lateral dispersivities affect the thermal stability and the dimensions of the convection cells. As a result of the convection currents the horizontal streamlines in the steady state are distorted. The thermal convection exhibits internal waves in the field.     

含混合裂隙、孔隙介质的纵波衰减规律研究

地下多孔介质中的孔隙类型复杂多样,既有硬孔又有扁平的软孔.针对复杂孔隙介质,假设多孔介质中同时含有球型硬孔和两种不同产状的裂隙(硬币型、尖灭型裂隙),当孔隙介质承载载荷时,考虑两种不同类型的裂隙对于孔隙流体压力的影响,建立起Biot理论框架下饱和流体情况含混合裂隙、孔隙介质的弹性波动方程,并进一步求取了饱和流体情况下仅由裂隙引起流体流动时的含混合裂隙、孔隙介质的体积模量和剪切模量,随后,在此基础上讨论了含混合裂隙、孔隙介质在封闭条件下地震波衰减和频散的高低频极限表达式.最后计算了给定模型的地震波衰减和频散,发现地震波衰减曲线呈现"多峰"现象,速度曲线为"多频段"频散.针对该模型分析讨论了渗透率参数、裂隙纵横比参数以及流体黏滞性参数对于地震波衰减和频散的影响,表明三个参数均为频率控制参数.     

Acoustic reflection well logging modeling using the frequency-domain finite-element method with a hybrid PML

In this paper, we propose a hybrid PML (H-PML) combining the normal absorption factor of convolutional PML (C-PML) with tangential absorption factor of Mutiaxial PML (M-PML). The H-PML boundary conditions can better suppress the numerical instability in some extreme models. and the computational speed of finite-element method and the dynamic range are greatly increased using this HPML. We use the finiteelement method with a hybrid PML to model the acoustic reflection of the interface when wireline and well logging while drilling (LWD), in a formation with a reflector outside the borehole. The simulation results suggests that the PS- and SP- reflected waves arrive at the same time when the inclination between the well and the outer interface is zero, and the difference in arrival times increases with increasing dip angle. When there are fractures outside the well, the reflection signal is clearer in the subsequent reflection waves and may be used to identify the fractured zone. The difference between the dominant wavelength and the model scale shows that LWD reflection logging data are of higher resolution and quality than wireline acoustic reflection logging.     

含孔隙、裂隙致密介质中多极子声波的传播特征

非常规油气藏（如致密性地层及蕴藏油气的页岩地层）的重要特征是低孔、低渗,但裂隙或裂缝比较发育.为满足非常规勘探的需求,本文将孔、裂隙介质弹性波传播理论应用于多极子声波测井的井孔声场模拟,重点研究了致密介质中裂隙发育时多极子声波的传播机理以及衰减特征.井孔声场的数值计算结果表明裂隙的存在明显改变了弹性波和井孔模式波的频散、衰减和激发强度,尤其是井壁临界折射纵波的激发谱的峰值随着频率的增加逐渐降低,这与应用经典的Biot理论下的计算结果相反,且裂隙的存在也使得饱含水和饱含气时临界折射纵波激发强度的差异变大.井孔模式波的衰减与地层横波衰减和井壁流体交换有关,井壁开孔边界下致密地层裂隙发育还使得井孔斯通利波和艾里相附近的弯曲波对孔隙流体的敏感性增强,在井壁闭孔边界条件下引起井孔模式波衰减的主要因素是裂隙引起的地层横波衰减造成的,且在截止频率附近弯曲波的衰减与地层的横波衰减一致.数值计算结果为解释非常规油气地层的声学响应特征提供了参考.     

Model of a porous medium with an elastic fractured skeleton

The model of a saturated porous medium with a brittle deformable skeleton is formulated in an isothermal approximation. The general form of governing equations is found, which is necessary and sufficient to fulfill the principles of objectivity and thermodynamic consistency. It is shown that the kinetics of developing the ensemble of microcracks, determined by the derivative of the elastic potential of the skeleton with respect to the fracture parameter, results in a nonnegative dissipation of the scattered destruction with any type of loading. For small deviations from the initial state, a new elastic potential is proposed which has made it possible to describe the main irregularities of the behavior of the medium in question. The solution of the problem about the consolidation of a saturated porous half-space with a brittle skeleton under a normal load has been constructed.     

Tidal deformations and the electrokinetic effect in a two-layer fluid-saturated porous medium

The electrokinetically induced vertical component of the electric field in a multilayer fluid-saturated porous medium caused by tidal deformations of the Earth’s crust is calculated. Petrophysical properties change in a jumplike manner at the boundary between two media. The pore pressure gradient at the boundary abruptly reaches a maximum and then exponentially decays, forming a hydrodynamic skin layer. Due to the electrokinetic effect, the electric field behaves in the same way. Observations of the vertical electric field can be used, in principle, to determine the mechanical properties of the medium experiencing deformation. The magnitudes of the effects lie within a range accessible to measurement.     

Analytical modeling of diffusion-limited contamination and decontamination in a two-layer porous medium

Diffusion of dissolved contaminants in multilayer porous media is an important phenomenon affecting both contamination and remediation in natural aqueous environments, including diffusion in groundwater aquitards and contaminated bed sediments. This study presents a new analytical solution for solute diffusion in a semi-infinite two-layer porous medium for arbitrary boundary and initial conditions. The solution was obtained by using the Green's function approach in the Laplace domain with the application of the binomial theorem to facilitate inversion back to the real time domain. Results based on this solution were found to be simple both in form and ease of calculation and to be in good agreement with those obtained using numerical calculations based on the Crank-Nicolson finite difference method. Applications of the solution are presented in the context of a contaminated groundwater aquitard to demonstrate how different boundary and initial conditions can greatly affect the contamination and decontamination of porous media, and to illustrate how diffusion modeling might be used in a forensic sense.     

基于Kelvin-Voigt黏弹性骨架的含非饱和流体孔隙介质BISQ模型(英文)

本文综合考虑了在波传播过程中孔隙介质的三种重要力学机制——"Biot流动机制一squirt流动机制-固体骨架黏弹性机制",借鉴等效介质思想,将含水饱和度引入波动力学控制方程,并考虑了不同波频率下孔隙流体分布模式对其等效体积模量的影响,给出了能处理含粘滞性非饱和流体孔隙介质中波传播问题的黏弹性Biot/squirt(BISQ)模型。推导了时间-空间域的波动力学方程组,由一组平面谐波解假设,给出频率-波数域黏弹性BISQ模型的相速度和衰减系数表达式。基于数值算例分析了含水饱和度、渗透率与频率对纵波速度和衰减的影响,并结合致密砂岩和碳酸盐岩的实测数据,对非饱和情况下的储层纵波速度进行了外推,碳酸盐岩储层中纵波速度对含气饱和度的敏感性明显低于砂岩储层。     

双轴各向异性介质多分量感应测井响应快速计算

为研究双轴各向异性介质多分量感应测井响应特征,本文基于三重傅里叶变换,推导任意方向偶极子源的谱域电磁场解析式;采用围线积分方法,自适应截断积分区间,结合谱域电磁场周期特性,实现三重傅里叶变换的精确快速积分;进而,针对双轴各向异性倾斜地层,模拟研究不同纵横向各向异性条件多分量感应测井响应特征.结果表明：利用谱域内电磁场在周向的周期特性简化解析式,可将计算速度提高4倍;自适应截断积分区间方法保证了计算精度,并极大地减少了积分节点数.对于倾斜双轴各向异性介质,倾角较大时,共面分量可反映地层横向各向异性,同轴分量可反映地层纵向各向异性;倾角较小时,同轴分量可反映地层横向各向异性,共面分量可反映地层纵向各向异性.

     

Direct parameter identification of fractured porous medium

A direct method of parameter identification for a fracture porous medium can be formulated. The coefficient of piezo-conductivity and the virtual fracture transmissivity can be determined using a combination of graphical methods and approximate formulae. Field calculation provides a practical demonstration of the proposed approach.     

Approximation of interfacial properties in multiphase porous medium systems

We investigate the estimation of interfacial areas, curvatures, and common curve lengths in multiphase porous medium systems. Algorithms are developed to obtain estimates of these quantities based upon a variety of potential data sources and estimation approaches. The accuracy of the derived approximations are evaluated as a function of the data type and resolution of the data. The methods advanced improve upon standard approaches now in use and show excellent accuracy at resolutions on the order of five lattice points per minimum radius of curvature of the object being resolved. Finally, we suggest a promising class of extensions that could lead to further improvements in the accuracy of such methods.     

含两项不混合/单项黏性流体孔隙介质分界面上反透射系数特征研究

弹性孔隙介质分界面上的反透射系数特征,在岩性划分、流体识别、储层边界判识等方面有重要的应用.本文研究上层为含两项不混合黏性流体孔隙介质、下层为含单项黏性流体孔隙介质分界面上的反透射理论.首先根据两种孔隙介质分界面上的能量守恒得到边界条件,再将波函数、位移、应力与应变关系代入边界条件,推导出完全连通孔隙情况下,第一类纵波入射到孔隙介质分界面上的反透射系数方程.通过建立砂岩孔隙介质模型,分别分析不同孔隙流体类型、不同含油饱和度及不同入射角情况下,各类波的反透射系数特征.研究表明,第二、三类纵波反透射系数数值比第一类纵波小多个数量级,且两者对入射角的变化不敏感,但对孔隙流体性质、含油饱和度的变化较敏感,而横波反透射系数特征恰好与此相反;第一类纵波反透射系数特征比较复杂,入射角、孔隙流体的性质及含油饱和度的变化都对其产生影响.不同孔隙流体弹性物性的差异、孔隙介质中含油饱和度的变化及不同入射角引起垂向和切向应力分量的变化都会影响各类波的反透射系数特征,分析这些特征可以为研究储层含油气性提供理论基础.

     

Full frequency-range transient solution for compressional waves in a fluid-saturated viscoacoustic porous medium1

An analytical transient solution is obtained for propagation of compressional waves in a homogeneous porous dissipative medium. The solution, based on a generalization of Biot's poroelastic equations, holds for the low- and high-frequency ranges, and includes viscoelastic phenomena of a very general nature, besides the Biot relaxation mechanism. The viscodynamic operator is used to model the dynamic behaviour associated with the relative motion of the fluid in the pores at all frequency ranges. Viscoelasticity is introduced through the standard linear solid which allows the modelling of a general relaxation spectrum. The solution is used to study the influence of the material properties, such as bulk moduli, porosity, viscosity, permeability and intrinsic attenuation, on the kinematic and dynamic characteristics of the two compressional waves supported by the medium. We also obtain snapshots of the static mode arising from the diffusive behaviour of the slow wave at low frequencies.