Permeability tensor and representative elementary volume of fractured rock masses

Based on a simulation of three-dimensional fracture networks and a superposition principle of liquid dissipation energy for fractured rock masses, a model of the fracture permeability tensor is proposed. An elastic constitutive model of rock fractures, considering fracture closure and dilation during shearing, is also proposed, based on the dilation angle of the fracture. Algorithms of flow-path searching and calculation of the effective flow coefficients for fracture networks are presented, together with a discussion on the influence of geometric parameters of the fractures (trace length, spacing, aperture, orientation and the number of fracture sets) on magnitude, anisotropy of hydraulic permeability and the size of a representative elementary volume (REV). The anisotropy of hydraulic permeability of fractured rock masses is mainly affected by orientation and the number of fracture sets, and the REV size is mainly influenced by trace length, spacing and the number of fracture sets. The results of studies on REV size and the influence of in-situ stress on hydraulic conductivity of the rock mass on the slope of Jinping-I hydropower station, China, are presented using the developed models and methods. The simulation results agreed well with the results obtained from field water-pressure measurements, with an error of less than 10 %.     

基于块体化程度确定裂隙岩体表征单元体

表征单元体（REV,或典型单元体）的存在是应用连续介质方法研究岩体问题的前提,因此,裂隙岩体表征单元体研究是岩体力学及岩体水力学中的一个基础问题,表征单元体的存在与否可以从不同物理参数的角度进行分析。从岩体块体化程度的角度对其存在性进行了较系统的分析,把岩体中由裂隙圈闭形成的孤立块体的总体积在岩体中所占体积百分比定义为裂隙岩体的块体化程度。介绍了GeneralBlock软件的基本分析过程,利用软件建立了三维裂隙岩体模型。根据国际岩石力学学会的裂隙分级,针对5个延展性级别、7个间距级别建立了35种岩体结构模型。利用GeneralBlock对这35种岩体进行了块体识别,分别讨论了这35种岩体结构的块体化程度随着模型范围变化的波动情况。由于所建立的岩体结构模型是随机的,对每种结构的每个研究范围进行了5次随机实现。结果表明,对所有的35种岩体,表征单元体的尺寸在4～8倍间距之间,不超过8倍间距。     

基于非均质系数的裂隙岩体表征单元体研究

表征单元体（REV）是岩体力学中的一个基础性概念,其存在性是确定岩体等效参数和应用连续介质方法进行研究的前提条件。为综合反映裂隙大小、产状和密度对岩体REV的影响,本文提出采用岩体非均质系数HI来确定岩体的REV。首先,详细介绍了非均质系数的概念和含义。利用General Block软件建立了中等间距-中等延展性（MS1-MP1）裂隙的网络模型,并完成20次随机实现。从各模型中选取10个不同尺寸的岩体模型计算非均质系数,结果表明：非均质系数具有明显的尺寸效应,当岩体尺寸不小于8 m时,非均质系数的平均值和标准差分别为0.5和0.14,综合确定该岩体的REV为8 m。采用HI对三峡地下电站厂房围岩的研究表明,该岩体的REV为60 m,可作为非连续介质方法适用性的判断标准。HI是从岩体结构角度提出的新指标,适用于确定岩体的REV和统计范围,对岩体的统计分析和等效参数研究具有重要意义。     

裂隙岩体表征单元体及尺寸效应研究进展

裂隙岩体的表征单元体（REV）是岩体力学中的一个基础性概念,一直是学者们关注的焦点。结合近年来的研究成果,对裂隙岩体表征单元体最新研究进展进行全面、详细地介绍,从表征单元体研究角度与参数、研究方法以及量化方法 3个主要方面进行阐述。将探讨裂隙岩体表征单元体的角度归纳为结构面及块体几何参数、岩体力学参数和水力学参数3个方面;研究方法主要包括统计学方法、解析法和数值分析法,对这些方法的研究现状进行介绍;最后对量化岩体REV尺度的常用方法进行概括总结,包括直观判断、误差及变异系数判别法、假设检验、曲线拟合法和灰关联分析。为相关研究提供一定的参考和指导。     

Structure of the low permeable naturally fractured geothermal reservoir at Soultz

The permeability of the granite geothermal reservoir of Soultz is primarily related to major fracture zones, which, in turn, are connected to dense networks of small-scale fractures. The small-scale fractures are nearly vertical and the major direction is about N0°E. This direction differs from that of the Rhine Graben, which is about N20°E to N45°E in northern Alsace. A total of 39 fracture zones, with a general strike of N160°E, have been identified in six wells between 1400 and 5000 m depth. These fracture zones are spatially concentrated in three clusters. The upper cluster at 1800–2000 m True Vertical Depth (TVD) is highly permeable. At 3000–3400 m TVD, the intermediate cluster in composed of a dense network developed in an altered matrix and forms the upper reservoir. In the lower part of the wells, the deeper cluster appears as a fractured reservoir developed within a low permeable matrix. Fracture zones represent a key element to take into account for predicting the geothermal reservoir life time submitted to various thermo-hydromechanical and chemical processes generated by hydraulic or chemical stimulations and by hydraulic circulation tests related to long-term exploitation.     

砂岩孔隙热储地温场水化学场特征及地热水富集机理——鲁北馆陶组热储典型案例

鲁北平原不同构造单元,具有不同温度、矿化度、特殊化学成分、富水性的地热资源。其中馆陶组热储是区内资源最丰富、开采利用程度最高、规模最大,为最具经济开采价值的热储。正确认识其地温场、水化学场特征及地热水富集机理,成为目前人们最为关心的问题。本文根据对馆陶组热储盖层地温梯度、热储温度变化特征的分析,结合地质构造条件,揭示了地温场温度受断裂构造影响,高温区主要分布在武城-高唐-陵县、宁津-庆云、沾化-孤岛、高青-博兴等凸起区与断裂交汇部位。区内馆陶组地热水化学类型以Cl-Na为主,其次为Cl·SO_4-Na及SO_4·Cl-Na型,矿化度4.07～18.52g/L,pH值7.14～8.1,地热水中含有大量人体健康所需的微量元素。分析认为,区内馆陶组地热水成因为大气降水,蒙脱石向绿泥石转变是地热水中贫钾、贫镁原因,馆陶组热储地热水总体流向为西南流向东北,在各县市城区地热水由四周向城区漏斗中心运移。本文根据地热钻探揭露馆陶组底砾岩深度、厚度及地热井水位、单井涌水量等大量数据的分析,揭示了鲁北平原馆陶组地热水古沉积相环境,并划分出两个大的古河道带:即临清—武城—德州—陵县一线古河道带和沾化—河口—仙河一线古河道带。前者后期受南部高唐凸起和东部埕子口-宁津潜断隆控制,在德州—陵县一带形成了范围较大、岩性颗粒较粗、厚度较大的冲洪积扇区;后者主要受西北部刁口潜凸起、义和庄潜凸起与南部无棣潜凸起控制,在河口—孤岛—仙河一带形成了较大范围岩性颗粒较粗、厚度较大的冲洪积扇区。在下游受陈庄凸起、青坨凸起影响,将古河道带分叉为两部分,南部古河道带分布在利津—东营一带。地热水富水规律与古河道带一致,富水区主要分布在两个古河道带区域,单井涌水量一般大于85m~3/h,且距古河道带越近,含水层砂砾岩埋藏越深,颗粒越粗,富水条件越好;反之,富水条件越差。在古河道带冲洪积扇部位富水条件最好。     

鲁北地区砂岩热储地热尾水回灌地温场变化特征分析

本文通过对德州水文家园砂岩热储地热回灌井全井段温度监测,在深度上分为5个区段论述了地温场的变化特征,重点对热储温度恢复的热量来源进行了分析。研究结果表明,在规模化生产性回灌时,低温地热尾水回灌会使得回灌井周边热储温度明显降低,并且恢复速率特别缓慢;通过定性分析和定量计算,认为大地传导热流和顶部地层传导热流在热储温度恢复中的作用极其微弱,而外围同层相对高温地层传导的热量和地热水流动带来的热量是其温度恢复的主要热量来源。基于该研究结果,在规模化回灌条件下,发生热突破是必然的,因此深入开展回灌工程采灌井合理井距研究、防止短时间内发生热突破是非常有必要的。     

有效应力对裂缝型低渗透砂岩油藏压力响应的影响

为了研究裂缝孔隙型低渗油藏中流体在双重介质之间的渗流规律及其影响,建立了双重介质间流体窜流的数学模型,并利用拉氏变换数值反演方法给出近似解析解;通过数值计算,研究窜流压力的动态特征,分析储容系数及窜流系数对压力响应的影响;通过压敏试验研究了有效应力对双重介质低渗油藏渗流能力的影响。研究结果表明：储容系数主要决定双重介质之间发生窜流现象的早晚,储容系数越大,发生窜流的时间越晚;储容系数越小,发生窜流的时间越早。窜流系数主要决定双重介质之间发生窜流压力的大小,窜流系数越大,发生窜流的压力越小;窜流系数越小,发生窜流的压力越大。有效应力对裂缝型低渗透油藏的渗流能力影响很大,有效应力的增加能够大大降低裂缝型油藏渗透率和孔隙度,以致降低储层的储容系数和窜流系数,从而影响双重介质间窜流压力的动态特征。因此,在裂缝型低渗透砂岩油藏开采中,保持压力、防止储层伤害是非常重要的。     

Contribution of the exploration of deep crystalline fractured reservoir of Soultz to the knowledge of enhanced geothermal systems (EGS)

Over the past 20 years, the Soultz experimental geothermal site in Alsace, France, has been explored in detail by the drilling of five boreholes, three of which extend to 5 km depth. Data on geology, fluid geochemistry, temperature, microseismicity, hydraulics and geomechanics have been collected and interpreted by the various teams from the participating European countries and their international collaborators. Two reservoirs have been developed within granite at depths of 3.5 and 5 km. The reservoir at 3.5 km was formed from two wells, 450 m apart, both of which were subjected to hydraulic stimulation injections. The system was circulated continuously for 4 months at 25 kg/s in 1997 using a downhole pump, and yielded results that were extremely encouraging. The impedance reduced to 0.1 MPa/l/s, the first time this long-standing target had been attained. Construction of a deeper system began shortly afterwards with the drilling of 3 deviated wells to 5 km true vertical depth, where the temperature was 200 °C. The wells were drilled in a line, 600 m apart at reservoir depth, and all were hydraulically stimulated and subjected to acidization injections. The 3-well system was circulated under buoyancy drive for 5 months in 2005 with injection in the central well, GPK-3, and production from the two outer wells, GPK-2 and GPK-4. This showed good linkage between one doublet pair, but not the other. Further acidization operations on the low-productivity well led to its productivity increasing to almost the same level as the other wells. Construction of a power plant at the site was completed in 2008 and a trial circulation with a production pump in one well and the other shut-in was conducted with power production. Downhole pumps are now installed in both production wells in preparation for long-term circulation of the system. In this article we present an overview of the principal accomplishments at Soultz over the past two decades, and highlight the main results, issues identified, and lessons learnt.     

砂岩热储回灌对储层影响评价——以鲁西北坳陷地热区为例

地热流体经供暖利用后尾水温度降低,经过滤、排气处理后的尾水中仍含有不同粒径的悬浮物、气体,因此回灌不可避免的会对储层造成负面影响,如堵塞储层导致回灌量衰减、热储温度降低甚至产生热突破等,这严重阻碍了地热回灌的长期可持续运行。评价回灌对储层的影响,对下一步全面推进、科学回灌及合理可持续开发利用、保护地热资源具有重要意义。本文以近几年鲁西北坳陷区开展的馆陶组热储回灌试验为基础,设立了一套评价指标,即用回灌前、后水质的变化率评价回灌对热储流体的影响,温度的变化率评价回灌对热储温度的影响,单位涌水量变化率、渗透系数的比值和单位回灌量比值评价回灌堵塞程度并确定了分级标准。评价结果表明,回灌不会改变储层流体的化学类型;回灌堵塞主要发生在回灌井周围,相比回灌前,回灌后回灌井的单位涌水量降低14.3%～59.0%、渗透系数为原来的41%～86%,末期单位回灌量为初期回灌量的51%～92%,回灌堵塞程度为轻度到严重。采灌井距180～500m,历经一个供暖季回灌对热储温度的影响较小,但回灌导致回灌井周边热储温度明显降低,历经一个非回灌期224d,从35. 7℃恢复到40. 53℃,恢复速率为0. 036～0. 022℃/d,还需658d才能恢复到原热储温度(55℃)。本区热储水位仍呈下降趋势,但回灌可延缓热储水位的下降速度。     

热储特征对砂岩热储采灌井距的影响

水热型地热资源的回灌式开采是公认的地热可持续开采方式,而采灌井距是地热项目中需要着重关注的问题,以避免开采井中的热突破现象。回灌水在热储中的运移取决于热储特征,也就是储层的透水能力,主要指热储的孔隙度、渗透率及砂泥岩组合关系等参数。基于济阳坳陷典型地热田的储层数据,采用Tough2为核心的Petrasim软件建立数值模型,系统研究了储层孔隙度、渗透率及单砂体厚度对热储中回灌水的运移以及温度场的影响。模拟结果显示：（1）储层孔隙度对回灌压力与采灌井距几乎没有影响;（2）储层渗透率对采灌率和采灌压力影响较大,控制着热储的回灌能力,但对采灌井距没有影响;（3）多次叠置的薄砂层热储中的泥岩隔层影响回灌水运移,在多层薄砂叠置的热储中回灌水水平运移距离远,温度影响范围更大,应扩大采灌井距。该研究对地热开发项目的可持续运行具有指导意义。     

基于分维数的土体裂隙表征单元体估算

由于干湿循环、剪切或其它作用,自然界土壤表面发育着大量裂隙。裂隙相互连接形成网络,裂隙网络是一个随机无序的系统,常规统计方法描述裂隙的分布特征存在很大的难度。网状土体裂隙一般具有分形特征,可以用分维数来进行描述。用数码相机拍摄土体表面的裂隙,将其转换成灰度图像,并结合分形理论,建立了摄影法测定土体裂隙分维数的方法,得到了土体裂隙的分维数。根据表征单元体的物理意义,建立了基于分维数估算表征单元体的方法,并对实例进行了分析。研究表明：分维数随裂隙密度,裂隙宽度和次一级裂隙发育程度的增大而增大;表征单元体与裂隙的密度均匀性和隙宽均匀性相关,基于分维数估算表征单元体的方法简便可行。     

Estimation of the REV size for blockiness of fractured rock masses

The representative elementary volume (REV) is the premise of the continuous-media method of analysis, and the investigation of the REVs of fractured rock masses is a fundamental area of rock mechanics research. The existence of an REV can be determined based on a variety of physical parameters. This paper presents an analysis of the REV from the view of blockiness, which is defined as the percentage of the volume of isolated blocks formed by fractures in the total rock volume. Seventy-seven types of fractured rock mass models were developed based on 7 classes of fracture persistence and 11 classes of spacing that are suggested by the International Society for Rock Mechanics (ISRM) fracture classification. Rock blocks in each of the 77 types of fractured rock mass models were identified using GeneralBlock to determine the variation in blockiness with model domain sizes, which were changed from 2 to 20 times the fracture spacing. For each model domain size 9 random realizations were carried out to reduce the effects of randomness. The coefficient of variation (C_v) was then used to quantify the variability of the 9 random realizations. The fluctuation in blockiness with the variation in the scale of the model region was also investigated. In this way, the size of the REV in these models can be calculated using the average and the variance of the blockiness as indicators of the convergence. The blockiness of these fractured rock masses can be determined at the REV volume. The results indicate that of the 77 models, 76 REV sizes are between 2 and 20 times the fracture spacing. The fractured rock mass with a wide fracture spacing and very high persistence (WS2–VHP) has a REV size that exceeds 20 times the fracture spacing. Thus, the WS2–VHP model should be investigated further to validate this concept.     

Thermohydrodynamic modeling of the natural state of the Mutnovsky geothermal reservoir (Kamchatka)

The paper presents results of modeling of the natural state of the Mutnovsky geothermal field (Kamchatka) developed to produce electric energy. The modeling was performed using the TOUGH2 program, currently the most perfect instrument for analyzing heat-and-mass transport in porous-fissured medium. It is based on the conceptual model of a geothermal reservoir based on previous investigations. The results confirmed the main statements of the conceptual model: location of heat sources, pattern of fluid flow in the reservoir, and location of the two-phase zone, and can serve as a basis for predicting the behavior of the Mutnovsky reservoir during its exploitation.     

Fluid-rock interactions in a geothermal Rotliegend/Permo-Carboniferous reservoir (North German Basin)

Comprehensive data on the chemical composition of reservoir rocks and geothermal brines from the geothermal well doublet Groβ Schönebeck (North German Basin) drilled into a Rotliegend sedimentary and Permo-Carboniferous volcanic rock reservoir were sampled over the past years. They were characterized with respect to their major and minor elemental composition including various isotope ratios. The study considered the impact of drilling and reservoir operations on fluid composition and aimed at determining fluid–rock interactions to gain information on fluid origin and hydraulic pathways.The highly saline fluids (up to 265 g/L TDS) show δ ¹⁸O and δD of water (2.7–5.6 and −3.1–15, respectively) as well as δ ³⁴S of sulfate (3.6–5), and ⁸⁷Sr/⁸⁶Sr ratios (0.715–0.716) that resemble Rotliegend brines from an area located around 200 km in the west (the Altmark). Halogen ratios indicated that brines developed predominantly by evaporation of meteoric water (primary brine) together with halite dissolution brine (secondary brine). Indication for mixing with Zechstein brine or with younger meteoric water was not found.No geochemical distinction was possible between fluids deriving from different rock formations (dacites or sedimentary rocks, respectively). This is due to the evolution of the sediments from the effusive rocks resulting in a similar mineralogical and chemical composition and due to a hydraulic connectivity between the two types of rock. This connection existed probably already before reservoir stimulation as indicated by a set of faults identified in the area that could connect the Rotliegend formation with both, the volcanic rocks and the lower units of the Zechstein. Additional geochemical indication for a hydraulic connectivity is given by (1) the very high heavy metal contents (mainly Cu and Pb) in fluids and scaling that derive from the volcanic rocks and were that were also found in increased amounts up at the Zechstein border (Kupferschiefer formation). (2) The ⁸⁷Sr/⁸⁶Sr isotope ratios of fluid samples correspond to the ratios determined for the sedimentary rocks indicating that initially the fluids developed in the sedimentary rocks and circulated later, when faults structures were created by tectonic events into the volcanic rocks.     

Delineating spring recharge areas in a fractured sandstone aquifer (Luxembourg) based on pesticide mass balance

A simple method to delineate the recharge areas of a series of springs draining a fractured aquifer is presented. Instead of solving the flow and transport equations, the delineation is reformulated as a mass balance problem assigning arable land in proportion to the pesticide mass discharged annually in a spring at minimum total transport cost. The approach was applied to the Luxembourg Sandstone, a fractured-rock aquifer supplying half of the drinking water for Luxembourg, using the herbicide atrazine. Predictions of the recharge areas were most robust in situations of strong competition by neighbouring springs while the catchment boundaries for isolated springs were extremely sensitive to the parameter controlling flow direction. Validation using a different pesticide showed the best agreement with the simplest model used, whereas using historical crop-rotation data and spatially distributed soil-leaching data did not improve predictions. The whole approach presents the advantage of integrating objectively information on land use and pesticide concentration in spring water into the delineation of groundwater recharge zones in a fractured-rock aquifer.     

致密砂岩储层与常规砂岩储层成藏动力学特征的差异性:以松辽盆地北部三肇地区扶余油层砂岩储层为例

为了研究三肇地区扶余油层砂岩储层特征,采用三维CT扫描技术和恒速压汞技术,对储层微观孔喉结构特征进行表征。结果表明,常规砂岩储层的孔喉大量发育,连通性好,为微米级孔喉。致密砂岩储层孔喉非均质性强,孤立零散分布,连通性差,以纳米级孔喉为主。微观孔喉特征的差异决定了油气充注、运移、聚集及渗流机理等成藏动力学特征具有差异性。通过对该区扶余油层砂岩储层的高压压汞实验、浮力与毛细管阻力公式计算及岩芯流动实验进行分析,认为油气在常规砂岩储层中初次运移动力是超压,二次运移及聚集的主要动力是浮力,油气以侧向运移为主,断层和砂体的匹配是主要的运移通道,流体流动状态呈达西渗流规律;油气在致密砂岩储层中运移动力为超压,油气以垂向运移为主,流体呈低速非达西渗流现象,以活塞-推挤的方式聚集。由于常规和致密油藏成藏动力学特征的差异,决定了油藏地质特征及分布的差异。三肇地区常规油藏主要是远距离、构造高部位聚集,上油下水规律明显,受构造控制;致密油藏主要是近距离、源下聚集,"甜点区"富集,圈闭边界不明显。     

Significance of shape factor on permeability anisotropy of sand: representative elementary volume study for pore-scale analysis

Acta Geotechnica - This paper is a study of determination of representative elementary volume (REV) size suitable for pore-scale flow simulation (PFS) and evaluation of permeability anisotropy for...     

Noble gas evidence for two fluids in the Baca (Valles Caldera) geothermal reservoir

Noble gas elemental and isotopic abundances were measured in steam from four wells in the Baca geothermal reservoir located in the Valles Caldera, New Mexico. The ${}^{40}\text{Ar}{}^{36}\text{Ar}$ ratio and noble gas elemental abundances relative to ³⁶Ar are all strongly correlated with 1/³⁶Ar, the inverse of the argon content. Ratios of (α,n)-produced ²¹Ne1 and radiogenic ⁴⁰Ar1 to total ⁴He (dominantly radiogenic) are nearly constant at 2.1 × 10?8 and 0.20, respectively. The ${}^3\text{He}{}^4\text{He}$ ratio covers a restricted range of 3.9 to 4.8 times atmospheric. The high ³He content of the gas indicates the presence of a helium component ultimately derived from the mantle. Kr and Xe isotopic compositions are close to atmospheric; excess ¹²⁹Xe1 is <0.25% of the total ¹²⁹Xe.The high degree of linear correlation among the various noble gas results strongly suggests that the Baca reservoir contains two distinct fluids that are produced in varying proportions from individual wells. The noble gases in fluid A (~2900 mg/1 C1) are air-like, but with lighter gases and isotopes preferentially enriched. The fluid A ³⁶Ar content is low, only 13% that of 10°C air-saturated water (ASW). The second fluid, B (~ 1700 mg/1 C1), is the dominant carrier of the radiogenic and mantle-derived gases. The heavier non-radiogenic gases are preferentially enriched in fluid B, and its ³⁶Ar content is very low, only 5–7% ASW. The source of the noble gases in fluid A is tentatively ascribed to leaching of the relatively young (<1.4 m.y.) volcanic Bandelier Tuff. The radiogenic gases and mantle-derived helium in fluid B suggest a deeper source, possibly including gases escaping from a magma.     

德州市德城区砂岩热储地热资源开采对地面沉降的影响

德城区是鲁西北砂岩热储地热资源开采的主要地区,地热水开采是否对地面沉降造成影响尚未开展研究,这将直接影响地方政府对地热资源开发的决策及规范管理.根据土体固结理论,在相同固结条件下,同等水位降幅,热储层有效应力增量占该层自重应力的比值远低于深层地下水开采层有效应力增量占该层自重应力的比值.结合钻孔资料,认为该区热储层为泥...