An analytical solution for heterogeneous and anisotropic anticline reservoirs under well injection

This study develops a mathematical model for describing the steady-state head response to fluid injection into a fully penetrating well in a heterogeneous and anisotropic anticline reservoir. In the model, the upper boundary of the anticline reservoir is approximated by a form of step change in reservoir thickness and the domain of the reservoir is divided into two regions with different hydraulic conductivities. By virtue of the properties of Fourier series, the method of separation of variables is employed to develop the analytical solution of the model.     

Changes in geophysical properties caused by fluid injection into porous rocks: analytical models

Analytical models are provided that describe how the elastic compliance, electrical conductivity, and fluid‐flow permeability of rocks depend on stress and fluid pressure. In order to explain published laboratory data on how seismic velocities and electrical conductivity vary in sandstones and granites, the models require a population of cracks to be present in a possibly porous host phase. The central objective is to obtain a consistent mean‐field analytical model that shows how each modeled rock property depends on the nature of the crack population. The crack populations are described by a crack density, a probability distribution for the crack apertures and radii, and the averaged orientation of the cracks. The possibly anisotropic nature of the elasticity, conductivity, and permeability tensors is allowed for; however, only the isotropic limit is used when comparing to laboratory data. For the transport properties of conductivity and permeability, the percolation effect of the crack population linking up to form a connected path across a sample is modeled. However, this effect is important only in crystalline rock where the host phase has very small conductivity and permeability. In general, the importance of the crack population to the transport properties increases as the host phase becomes less conductive and less permeable.     

One-dimensional dispersion in unsteady flow in an adsorbing porous medium: An analytical solution

Analytical solutions describing the concentration distribution along one-dimensional unsteady seepage flow through adsorbing saturated finite porous medium have been obtained. An exponential function concentration is enforced at the source of the dispersion, while the change in the concentration is zero at the other boundary. A new time variable has been introduced to solve the unsteady flow problem and the solution is illustrated.     

成像测井解释模式在基岩油气藏裂缝性储层的应用研究

基岩油气藏裂缝性储层具有复杂的储集空间和储层非均质性,为了实现对基岩油气藏储层的精细评价,以地层微电阻率扫描成像测井和井周声波成像测井资料为核心,通过岩心资料标定,结合录井、常规测井、试油、地质等实际资料,系统建立了基岩油气藏变质岩储层的成像测井解释模式.根据成像测井模式的识别实现了对基岩油气藏特征的认识、准确的裂缝分析和现今地应力场分析.分析结果表明,研究区基底变质岩地层中基本以基岩内幕油气藏为主;裂缝以中高角度缝、网状裂缝为主,其主要走向与井旁断层走向大致平行,属纵裂缝;裂缝主要发育在东西两侧靠近断层、近源的构造陡坡上;现今最大水平主应力方向主要呈NE-SW和NEE-SWW.成像测井解释结果与地质情况吻合较好.     

Stochastic and analytical approaches for sediment accumulation in river reservoirs

ABSTRACT

Sediment accumulation in a river reservoir is studied by stochastic time series models and analytical approach. The first-order moving average process is found the best for the suspended sediment discharge time series of the Juniata River at Newport, Pennsylvania, USA. Synthetic suspended sediment discharges are first generated with the chosen model after which analytical expressions are derived for the expected value and variance of sediment accumulation in the reservoir. The expected value and variance of the volume of sediment accumulation in the reservoir are calculated from a thousand synthetic time series each 38 years long and compared to the analytical approach. Stochastic and analytical approaches perfectly trace the observation in terms of the expected value and variability. Therefore, it is concluded that the expected value and variance of sediment accumulation in a reservoir could be estimated by analytical expressions without the cost of synthetic data generation mechanisms.     

Establishment and application of logging saturation interpretation equation in vuggy reservoirs

Vuggy reservoirs are the most common, albeit important heterogeneous carbonate reservoirs in China. However, saturation calculations using logging data are not well developed, whereas Archie method is more common. In this study, electrical conduction in a vuggy reservoir is theoretically analyzed to establish a new saturation equation for vuggy reservoirs. We found that vugs have a greater effect on saturation than resistivity, which causes inflection in the rock-electricity curve. Using single-variable experiments, we evaluated the effects of vug size, vug number, and vug distribution on the rock-electricity relation. Based on the general saturation model, a saturation equation for vuggy reservoirs is derived, and the physical significance of the equation parameters is discussed based on the seepage-electricity similarity. The equation parameters depend on the pore structure, and vugs and matrix pore size distribution. Furthermore, a method for calculating the equation parameters is proposed, which uses nuclear magnetic resonance (NMR) data to calculate the capillary pressure curve. Field application of the proposed equation and parameter derivation method shows good match between calculated and experimental results, with an average absolute error of 5.8%.     

Consequences of induced polarization in magneto-telluric interpretation

Summary Both in-situ and laboratory studies indicate that naturally occurring earth materials are electrically dispersive. A review of both historical and recent developments in the field of dispersion is presented, including induced polarization (IP) as used in mineral prospecting. Computer-simulated magnetotelluric (MT) sounding curves are presented for nondispersive, semi-dispersive and dispersive, electrical structures. Admittivities of the form =A +A log (/₀)and other frequency dependent forms are used in the calculations. The results indicate that interpretation of electromagnetic field data, in terms of nondispersive layered structures, can lead to significant errors in the estimation of subsurface structure. Thus, there may be an important limitation in the use of variable frequency or transient data in the currently popular inversion schemes.     

平面SV波在饱和土半空间中圆柱形孔洞周边的散射

在Biot饱和多孔介质动力学理论的基础上,利用Fourier—Bessel级数展开法,得到SV波在饱和土半空间中圆柱形孔洞周边的散射问题的解析解答。与已有相关问题的解析解答进行对比,验证了此解的正确性,并给出算例,分析了入射频率对柱面上的应力集中因子的影响。     

裂缝型碳酸盐岩储层测井评价方法--以塔河油田为例

裂缝型碳酸盐岩储集层的测井解释一直是测井解释所面临的难题之一.本文较为系统地介绍了一种从提取和优化裂缝指标、计算裂缝概率、评价裂缝概率可信度到计算综合裂缝概率的测井解释方法.在研究中,提取密度\|中子孔隙度差异指标和FMI测井裂缝参数指标,并采用R型聚类分析,对常规测井裂缝指标和FMI测井裂缝参数指标进行优化,形成了优化的裂缝指标集;提出裂缝概率可信度评价的方法.最后,利用本文提出的解释方法,给出了塔河油田两口井的处理结果.     

P-wave dispersion and attenuation in fractured and porous reservoirs – poroelasticity approach

Natural fractures in hydrocarbon reservoirs can cause significant seismic attenuation and dispersion due to wave induced fluid flow between pores and fractures. We present two theoretical models explicitly based on the solution of Biot's equations of poroelasticity. The first model considers fractures as planes of weakness (or highly compliant and very thin layers) of infinite extent. In the second model fractures are modelled as thin penny-shaped voids of finite radius. In both models attenuation is a result of conversion of the incident compressional wave energy into the diffusive Biot slow wave at the fracture surface and exhibits a typical relaxation peak around a normalized frequency of about 1. This corresponds to a frequency where the fluid diffusion length is of the order of crack spacing for the first model and the crack diameter for the second. This is consistent with an intuitive understanding of the nature of attenuation: when fractures are closely and regularly spaced, the Biot's slow waves produced by cracks interfere with each other, with the interference pattern controlled by the fracture spacing. Conversely, if fractures are of finite length, which is smaller than spacing, then fractures act as independent scatterers and the attenuation resembles the pattern of scattering by isolated cracks. An approximate mathematical approach based on the use of a branching function gives a unified analytical framework for both models.     

An interpretation of induced electric currents in long pipelines caused by natural geomagnetic sources of the upper atmosphere

Electric currents in long pipelines can contribute to corrosion effects that limit the pipe's lifetime. One cause of such electric currents is the geomagnetic field variations that have sources in the Earth's upper atmosphere. Knowledge of the general behavior of the sources allows a prediction of the occurrence times, favorable locations for the pipeline effects, and long-term projections of corrosion contributions. The source spectral characteristics, the Earth's conductivity profile, and a corrosion-frequency dependence limit the period range of the natural field changes that affect the pipe. The corrosion contribution by induced currents from geomagnetic sources should be evaluated for pipelines that are located at high and at equatorial latitudes. At midlatitude locations, the times of these natural current maxima should be avoided for the necessary accurate monitoring of the pipe-to-soil potential.     

An analytical solution to wave dissipation induced by interacting waves and currents with muddy deposits

Ocean Dynamics - The present study aims to provide a straightforward analytical solution to wave-current-mud interaction by considering the mean shear stress effects in the water layer. A direct...     

各向异性衰减薄层地震响应特征研究

薄储层的叠前地震响应特征研究,特别是针对具有速度各向异性的含流体薄层,对储层描述具有十分重要的意义.文中基于波动方程数值模拟方法,正演得到各向同性弹性、各向同性衰减、速度各向异性、各向异性衰减模型的地震波场,并对比分析了四种模型的纵波（PP）和转换横波（PS）地震反射特征.研究结果表明：在衰减介质背景下,引入各向异性,PP和PS波的反射波振幅较弹性介质均减弱,且衰减因素对薄层振幅的影响强于各向异性.同时,VTI各向异性衰减在单频PS振幅曲线上表现出强差异性,而HTI各向异性衰减则会影响PP和PS波单频振幅曲线的极值点幅值和位置,通过分析单频振幅曲线的极值点振幅和极值点位置对各向异性衰减薄层预测有指导作用,尤其对平时较难分辨的VTI各向异性衰减薄层,单频分析方法的优势更明显.

     

An analytical solution for flow in a manifold

An analytical solution is developed for flow in a manifold. The interest is primarily for trickle irrigation laterals, but the solution has broader applications including those for which pressure increases in the direction of flow and for intake manifolds. Both velocity head losses and variable discharge along the manifold are considered in the fundamental analysis. The appropriate second order, nonlinear equation is solved for two flow regimes, laminar and fully turbulent. Results indicate that for most trickle irrigation laterals the velocity head loss is negligible, but for an example from a chemical processing system the effect is important.     

一种分析岩土模型地震受力变形的方法

在国内外岩土模型动力试验中,一般以图表形式对监测区域进行逐一动态分析,无法直观形象的掌握试验模型整体受力变形,为深入分析动态响应机理带来一定的不便。以前-后排抗滑桩加固斜坡桥基的大型振动台模型试验为例,通过在岩土体中埋设一定数量的自制磷青铜带和水平加速度计,监测滑坡变形和加速度响应,结合已知测点的水平坐标和竖向坐标,利用Renka Cline随机矩阵生成方法转换为数字矩阵形式,据此绘制坡体变形及PGA放大系数的二维等势图。试验结果显示,二维等势图能合理反映斜坡PGA放大系数的变化规律,揭示振动波作用下斜坡变形破坏的基本特征,研究结论和试验现象保持一致,满足斜坡模型整体受力变形分析的基本要求,可以作为一种实用的试验分析方法。     

Thermal coupling may control mechanical stability of geothermal reservoirs during cold water injection

Hydraulic stimulation and geothermal reservoir operation may compromise the rock mechanical stability and trigger microseismic events. The mechanisms leading to this induced seismicity are still not completely understood. It is clear that injection causes an overpressure that reduces the effective stress, bringing the system closer to failure conditions. However, rock instability may not result only from hydraulic effects, but also from thermal effects. In fact, hydro-mechanical (i.e., isothermal) models often fail to reproduce field observations because the injection of cold water into a hot reservoir induces thermal stresses due to rock contraction. Thus, rock instability is likely to result from the superposition of hydraulic and thermal effects. Here, we perform coupled thermo-hydro-mechanical and hydro-mechanical simulations to investigate the effects of cold water injection in a fracture zone-intact rock system. Results show that thermal effects induce a significant perturbation on the stress in the intact rock affected by the temperature drop. This perturbation is likely to trigger induced seismicity in the surroundings of critically oriented fractures near the injection well. Hydro-mechanical simulations show that the behavior depends on the orientation of the faults and on the initial stress tensor. In the direction of the fractures, where the strains are more constrained, total stress increases with increasing pressure; thus, deviatoric stress increases or decreases depending on the initial stress state. The comparison between hydraulic and thermal effects shows that, when the largest confining stress acts perpendicular to the fractures, thermoelastic effects dominate and could trigger induced seismicity.     

An analytical solution to study substrate-microbial dynamics in soils

We provide an approximate analytical solution for the substrate-microbial dynamics of the organic carbon cycle in natural soils under hydro-climatic variable forcing conditions. The model involves mass balance in two carbon pools: substrate and biomass. The analytical solution is based on a perturbative solution of concentrations, and can properly reproduce the numerical solutions for the full non-linear problem in a system evolving towards a steady state regime governed by the amount of labile carbon supplied to the system. The substrate and the biomass pools exhibit two distinct behaviors depending on whether the amount of carbon supplied is below or above a given threshold. In the latter case, the concentration versus time curves are always monotonic. Contrarily, in the former case the C-pool concentrations present oscillations, allowing the reproduction of non-monotonic small-scale biomass concentration data in a natural soil, observed so far only in short-term experiments in the rhizosphere. Our results illustrate the theoretical dependence of oscillations from soil moisture and temperature and how they may be masked at intermediate scales due to the superposition of solutions with spatially variable parameters.     

Research on earthquakes induced by water injection in China

In China, the earthquakes induced by water injection have occurred in four oil fields including the Renqiu oil field, and in two mines. Production of oil from the Renqiu oil field began in 1975 and the injection of water into the oil field commenced in July 1976. The induced earthquakes have been occurring in the area for the past 17 years, since December 1976. The controlled experiments of water injection showed the cause and effect relation between water injection and earthquakes. Source parameters such as source dimension, seismic moment and stress drop of a large number of the induced earthquakes, andQ factor for the area have been determined. The results indicate that the stress drop varies from 0.2 to 3.0 bar and theQ factor has an average value of 75.0. The low-stress drop and lowQ factor values imply that the earthquakes are caused by the brittle fracture of weak rocks under low ambient stresses, due to a decrease in their strength because of the injection of water. The induced earthquakes are unevenly distributed in the oil field. The northern part of the oil field, where the reservoir rocks are characterized by low porosity and low permeability, exhibits high seismic activity with the largest earthquake registering a magnitude of 4.5 and about 68% of the total number of induced earthquakes in this part. Whereas, the southern part of the oil field with higher porosity and higher permeability is characterized by low seismic activity with the largest earthquake registering a magnitude of 2.5 and only 4% of the total number of earthquakes which occurred in this part. These features of the focal region suggest that larger earthquakes may not occur in the Renqiu oil field area.     

四川省理县西山村滑坡运动变形过程中的微震研究

西山村滑坡位于地震活动性剧烈的龙门山地区,这个区域有大量的滑坡在汶川地震中被触发,此后西山村滑坡发生持续变形.为了监测该滑坡体的运移和局部破裂产生的微弱的地震信号,由微震事件获取滑坡滑动和变形模式,2015年八月底至十一月底,我们在滑坡上布置了30套地震仪.首先通过信号到时和波形特征把滑坡上的微震信号从人类活动产生的信号和滑坡体以外的区域地震信号区分开来.然后以识别到的微震波形为模板,用滑动时窗互相关的方法匹配其他的微震事件.结果表明,96个微震事件能被30个台站都记录到.通过对这些事件的定位,我们发现大部分（80个）能被所有台站记录到的事件发生在滑坡的底部,其他的少部分（16个）发生在滑坡的顶部.这意味着有相当多的能量积聚在滑坡的顶部和底部,而滑坡的底部则更活跃.除此外,在滑坡的中部有较多更微弱的事件被周围的部分仪器记录到.基于这些微震事件的位置,我们发现四个辐射地震信号的不稳定区域和钻孔监测到的不稳定区域比较吻合.这些辐射地震信号的不稳定区域应该和滑坡体的运动和内部变形相关.由此表明,地震学方法也是监测滑坡的变形的有效手段,是现有监测手段的有力补充.