Fractal generation of surface area of porous media

Many natural porous geological rock formations, as well as engineered porous structures, have fractal properties, i.e., they are self-similar over several length scales. While there have been many experimental and theoretical studies on how to quantify a fractal porous medium and on how to determine its fractal dimension, the numerical generation of a fractal pore structure with predefined statistical and scaling properties is somewhat scarcer. In the present paper a new numerical method for generating a three-dimensional porous medium with any desired probability density function (PDF) and autocorrelation function (ACF) is presented. The well-known Turning Bands Method (TBM) is modified to generate three-dimensional synthetic isotropic and anisotropic porous media with a Gaussian PDF and exponential-decay ACF. Porous media with other PDF's and ACF's are constructed with a nonlinear, iterative PDF and ACF transformation, whereby the arbitrary PDF is converted to an equivalent Gaussian PDF which is then simulated with the classical TBM. Employing a new method for the estimation of the surface area for a given porosity, the fractal dimensions of the surface area of the synthetic porous media generated in this way are then measured by classical fractal perimeter/area relationships. Different 3D porous media are simulated by varying the porosity and the correlation structure of the random field. The performance of the simulations is evaluated by checking the ensemble statistics, the mean, variance and ACF of the simulated random field. For a porous medium with Gaussian PDF, an average fractal dimension of approximately 2.76 is obtained which is in the range of values of actually measured fractal dimensions of molecular surfaces. For a porous medium with a non-Gaussian quadratic PDF the calculated fractal dimension appears to be consistently higher and averages 2.82. The results also show that the fractal dimension is neither strongly dependent of the porosity nor of the degree of anisotropy assumed.     

Volume changes during fracture and frictional sliding: A review

Summary Volume changes in geologic materials have been measured with strain gauges, cantilever displacement gauges, or through observation of either pore or total volume. When porosity is less than 0.05, compaction is small or absent; apart from elastic strains in the minerals, dilatancy predominates, beginning at 50 to 75 percent of the fracture stress difference. When initial porosity exceeds about 0.05, compaction and dilatancy may overlap. The onset of dilatancy has not been identified, but most of the dilatancy occurs within about 10 percent of the fracture stress difference. In low porosity rocks, dilatancy increases initial porosity by a factor of 2 or more; in porous rocks or granular aggregates the increase is only 20 to 50 percent. However, the actual pore volume increase is larger in rocks of high initial porosity. Hence, earthquake precursors which depend on the magnitude of dilatancy should be more pronounced in porous rocks or in fault gouge. In contrast, precursors which are based on fractional changes in some porosity-related property may be more pronounced in rocks of low initial porosity. Future work is particularly needed on constitutive relations suitable for major classes of rocks, on the effects of stress cycling in porous rocks, on the effects of high temperature and pore fluids on dilatancy and compaction, and on the degree of localization of strain prior to fracture.     

A fractal model for streaming potential coefficient in porous media

Streaming potential is the result of coupling between a fluid flow and an electric current in porous rocks. The modified Helmholtz–Smoluchowski equation derived for capillary tubes is mostly used to determine the streaming potential coefficient of porous media. However, to the best of our knowledge, the fractal geometry theory is not yet applied to analyse the streaming potential in porous media. In this article, a fractal model for the streaming potential coefficient in porous media is developed based on the fractal theory of porous media and on the streaming potential in a capillary. The proposed model is expressed in terms of the zeta potential at the solid?liquid interface, the minimum and maximum pore/capillary radii, the fractal dimension, and the porosity of porous media. The model is also examined by using another capillary size distribution available in published articles. The results obtained from the model using two different capillary size distributions are in good agreement with each other. The model predictions are then compared with experimental data in the literature and those based on the modified Helmholtz–Smoluchowski equation. It is shown that the predictions from the proposed fractal model are in good agreement with experimental data. In addition, the proposed model is able to reproduce the same result as the Helmholtz–Smoluchowski equation, particularly for high fluid conductivity or large grain diameters. Other factors influencing the streaming potential coefficient in porous media are also analysed.     

Fractal generation of surface area of porous media

Many natural porous geological rock formations, as well as engineered porous structures, have fractal properties, i.e., they are self-similar over several length scales. While there have been many experimental and theoretical studies on how to quantify a fractal porous medium and on how to determine its fractal dimension, the numerical generation of a fractal pore structure with predefined statistical and scaling properties is somewhat scarcer. In the present paper a new numerical method for generating a three-dimensional porous medium with any desired probability density function (PDF) and autocorrelation function (ACF) is presented. The well-known Turning Bands Method (TBM) is modified to generate three-dimensional synthetic isotropic and anisotropic porous media with a Gaussian PDF and exponential-decay ACF. Porous media with other PDF's and ACF's are constructed with a nonlinear, iterative PDF and ACF transformation, whereby the arbitrary PDF is converted to an equivalent Gaussian PDF which is then simulated with the classical TBM. Employing a new method for the estimation of the surface area for a given porosity, the fractal dimensions of the surface area of the synthetic porous media generated in this way are then measured by classical fractal perimeter/area relationships. Different 3D porous media are simulated by varying the porosity and the correlation structure of the random field. The performance of the simulations is evaluated by checking the ensemble statistics, the mean, variance and ACF of the simulated random field. For a porous medium with Gaussian PDF, an average fractal dimension of approximately 2.76 is obtained which is in the range of values of actually measured fractal dimensions of molecular surfaces. For a porous medium with a non-Gaussian quadratic PDF the calculated fractal dimension appears to be consistently higher and averages 2.82. The results also show that the fractal dimension is neither strongly dependent of the porosity nor of the degree of anisotropy assumed.     

含湿孔隙岩石有效热导率的数值分析

本文采用有限元方法研究含湿孔隙岩石的有效热导率,即随机划分网格并指定材料性质,建立三维含湿孔隙岩石的有限元模型,模型的上下表面施加不同的温度,侧面绝热,计算出总热流,然后结合上下表面的温度梯度计算出岩石的有效热导率.考虑到单个随机模型不一定具有代表性,对给定的孔隙率和饱和度均生成了200种矿物、水、空气随机分布的岩石模型,进行Monte Carlo实验和统计分析,统计分析结果与前人实验结果吻合良好.数值分析结果表明,孔隙岩石的有效热导率与岩石的孔隙率、饱和度、固体矿物组分及孔隙的分布情况有关,数值计算的误差随着网格数目的增加而减小.此有限元方法可以用来估算岩石的有效热导率,在已知组分性质的多矿物岩石物性计算方面有广阔应用前景.     

Pore size distributions and hydraulic conductivities of rocks derived from Magnetic Resonance Sounding relaxation data using multi-exponential decay time inversion

In hydrogeology there is a variety of empirical formulae available for determination of hydraulic conductivity of porous media, all based on the analysis of grain size distributions of aquifer materials. Sensitivity of NMR measurements to pore sizes makes it a good indicator of hydraulic conductivity. Analogous to laboratory NMR, Magnetic Resonance Sounding (MRS) relaxation data are of a multi-exponential (ME) nature due to the distribution of different pore sizes in an investigated rock layer. ME relaxation behaviour will also arise due to the superposition of NMR signals which originate from different layers. It has been shown, that both kinds of ME behaviour coexist in MRS and can principally be separated by ME inversion of the field data. Only a few publications exist that have proposed approaches to qualitatively and quantitatively estimate petrophysical parameters such as the hydraulic conductivity from MRS measurements, i.e. MRS porosity and decay times. The so far used relations for the estimation of hydraulic conductivity in hydrogeology and NMR experiments are compared and discussed with respect to their applicability in MRS. Taking into account results from a variety of laboratory NMR and MRS experiments mean rock specific calibration factors are introduced for a data-base-calibrated estimation of hydraulic conductivity when no on-site calibration of MRS is available. Field data have been analysed using conventional and ME inversion using such mean calibration values. The results for conventional and ME inversion agree with estimates obtained from well core analysis for shallow depths but are significantly improved using a ME inversion approach for greater depths.     

Pore size distributions and hydraulic conductivities of rocks derived from Magnetic Resonance Sounding relaxation data using multi-exponential decay time inversion

In hydrogeology there is a variety of empirical formulae available for determination of hydraulic conductivity of porous media, all based on the analysis of grain size distributions of aquifer materials. Sensitivity of NMR measurements to pore sizes makes it a good indicator of hydraulic conductivity. Analogous to laboratory NMR, Magnetic Resonance Sounding (MRS) relaxation data are of a multi-exponential (ME) nature due to the distribution of different pore sizes in an investigated rock layer. ME relaxation behaviour will also arise due to the superposition of NMR signals which originate from different layers. It has been shown, that both kinds of ME behaviour coexist in MRS and can principally be separated by ME inversion of the field data. Only a few publications exist that have proposed approaches to qualitatively and quantitatively estimate petrophysical parameters such as the hydraulic conductivity from MRS measurements, i.e. MRS porosity and decay times. The so far used relations for the estimation of hydraulic conductivity in hydrogeology and NMR experiments are compared and discussed with respect to their applicability in MRS. Taking into account results from a variety of laboratory NMR and MRS experiments mean rock specific calibration factors are introduced for a data-base-calibrated estimation of hydraulic conductivity when no on-site calibration of MRS is available. Field data have been analysed using conventional and ME inversion using such mean calibration values. The results for conventional and ME inversion agree with estimates obtained from well core analysis for shallow depths but are significantly improved using a ME inversion approach for greater depths.     

基于沉积过程的数字岩石建模方法研究

本文提出模拟地层沉积及成岩过程的矿物沉积算法,建立数字岩石模型,并通过对比Micro-CT扫描图像和数值模型的局部孔隙度及平均渗流概率函数分布特征,评价建模的准确性.结果表明,由二维扫描提取的粒径信息作为输入参数,模拟矿物沉积过程建模得到的三维数字岩石模型,能够准确重构原始岩心的非均质性及渗流特性,成功应用于泥质砂岩、碳酸盐岩、页岩等存在多矿物或多尺度孔隙的数字岩石建模中.数字岩石物理是正在兴起的重要技术.数字岩石采用超高分辨率先进成像装备,采集和表征微纳尺度岩石结构,在岩石弹性、电性、核磁、渗流特性等数值计算中发挥重要作用.但是,由于三维直接成像在有限视域内难以表征足够的岩石非均质性,提取二维结构统计特征,利用统计或地质过程法重构具有代表性的三维岩石结构成为十分有价值的研究课题,而且,对业界大量存在的岩石薄片及电镜高清二维图像的深度开发应用也具有重要的现实意义.本文发展的新方法,复原沉积过程,较好地解决了孔隙尺度岩石物理定量研究中数值建模与理论计算的技术瓶颈.     

砂砾岩储层测井评价研究

砂砾岩储层岩性复杂、非均质性强,储层间非渗透性隔层类型多,储层基质孔隙度有时很低,从而使测井资料准确划分有效储层有很大的难度;砂砾岩体储层母岩类型变化大,岩石骨架参数很难确定,电阻率测量受岩石骨架、粘土含量和孔隙结构影响严重,反映储层孔隙流体性质的信息弱,使储层流体性质难以判断,油、气、干层界限的电性特征极不明显.通过核磁共振和井壁微电阻扫描成像测井,可以直观观察到岩石成分和粒径的变化,通过T2谱分布直观显示核磁测量井段的孔径分布,计算出各种类型孔隙度和渗透率参数,为砂砾岩有效划分储层和测井评价提供了可靠的依据.     

Deep learning long short-term memory combined with discrete element method for porosity prediction in gravel-bed rivers

The porosity of gravel riverbed material often is an essential parameter to estimate the sediment transport rate, groundwater-river flow interaction, river ecosystem, and fluvial geomorphology. Current methods of porosity estimation are time-consuming in simulation. To evaluate the relation between porosity and grain size distribution (GSD), this study proposed a hybrid model of deep learning Long Short-Term Memory (LSTM) combined with the Discrete Element Method (DEM). The DEM is applied to model the packing pattern of gravel-bed structure and fine sediment infiltration processes in three-dimensional (3D) space. The combined approaches for porosity calculation enable the porosity to be determined through real time images, fast labeling to be applied, and validation to be done. DEM outputs based on the porosity dataset were utilized to develop the deep learning LSTM model for predicting bed porosity based on the GSD. The simulation results validated with the experimental data then segregated into 800 cross sections along the vertical direction of gravel pack. Two DEM packing cases, i.e., clogging and penetration are tested to predict the porosity. The LSTM model performance measures for porosity estimation along the z-direction are the coefficient of determination (R²), root mean squared error (RMSE), and mean absolute error (MAE) with values of 0.99, 0.01, and 0.01 respectively, which is better than the values obtained for the Clogging case which are 0.71, 0.14, and 0.03, respectively. The use of the LSTM in combination with the DEM model yields satisfactory results in a less complex gravel pack DEM setup, suggesting that it could be a viable alternative to minimize the simulation time and provide a robust tool for gravel riverbed porosity prediction. The simulated results showed that the hybrid model of the LSTM combined with the DEM is reliable and accurate in porosity prediction in gravel-bed river test samples.     

Simulation of less‐mobile porosity dynamics in contrasting sediment water interface porous media

Considering heterogeneity in porous media pore size and connectivity is essential to predicting reactive solute transport across interfaces. However, exchange with less‐mobile porosity is rarely considered in surface water/groundwater recharge studies. Previous research indicates that a combination of pore‐fluid sampling and geoelectrical measurements can be used to quantify less‐mobile porosity exchange dynamics using the time‐varying relation between fluid and bulk electrical conductivity. For this study, we use macro‐scale (10 s of cm) advection–dispersion solute transport models linked with electrical conduction in COMSOL Multiphysics to explore less‐mobile porosity dynamics in two different types of observed sediment water interface porous media. Modeled sediment textures contrast from strongly layered streambed deposits to poorly sorted lakebed sands and cobbles. During simulated ionic tracer perturbations, a lag between fluid and bulk electrical conductivity, and the resultant hysteresis, is observed for all simulations indicating differential loading of pore spaces with tracer. Less‐mobile exchange parameters are determined graphically from these tracer time series data without the need for inverse numerical model simulation. In both sediment types, effective less‐mobile porosity exchange parameters are variable in response to changes in flow direction and fluid flux. These observed flow‐dependent effects directly impact local less‐mobile residence times and associated contact time for biogeochemical reaction. The simulations indicate that for the sediment textures explored here, less‐mobile porosity exchange is dominated by variable rates of advection through the domain, rather than diffusion of solute, for typical low‐to‐moderate rate (approximately 3–40 cm/day) hyporheic fluid fluxes. Overall, our model‐based results show that less‐mobile porosity may be expected in a range of natural hyporheic sediments and that changes in flowpath orientation and magnitude will impact less‐mobile exchange parameters. These temporal dynamics can be assessed with the geoelectrical experimental tracer method applied at laboratory and field scales.     

复杂孔隙储层三维岩石物理模版

复杂孔隙储层往往同时发育孔缝洞等多种孔隙类型,这种孔隙结构的复杂性使得岩石的速度与孔隙度之间的相关性很差.经典的二维岩石物理模版只研究弹性参数与孔隙度和饱和度之间的定量关系,而不考虑孔隙结构的影响,用这样的模版来预测复杂孔隙储层的物性参数时带来很大偏差.本文首先证明多重孔隙岩石的干骨架弹性参数可以用一个等效孔隙纵横比的单重孔隙岩石物理模型来模拟;进而基于等效介质岩石物理理论和Gassmann方程,建立一个全新的三维岩石物理模版,用它来建立复杂孔隙岩石的弹性性质与孔隙扁度及孔隙度和饱和度之间的定量关系;在此基础上,预测复杂储层的孔隙扁度、孔隙度以及孔隙中所包含的流体饱和度.实际测井和地震反演数据试验表明,三维岩石物理模版可有效提高复杂孔隙储层参数的预测精度.     

Geostatistical modeling of clay spatial distribution in siliciclastic rock samples using the plurigaussian simulation method

In order to implement secondary and enhanced oil recovery processes in complex terrigenous formations as is usual in turbidite deposits, a precise knowledge of the spatial distribution of shale grains is a crucial element for the fluid flow prediction. The reason of this is that the interaction of water with shale grains can significantly modify their size and/or shape, which in turn would cause porous space sealing with the subsequent impact in the flow. In this work, a methodology for stochastic simulations of spatial grains distributions obtained from scanning electron microscopy images of siliciclastic rock samples is proposed. The aim of the methodology is to obtain stochastic models would let us investigate the shale grain behavior under various physico-chemical interactions and flux regimes, which in turn, will help us get effective petrophysical properties (porosity and permeability) at core scale. For stochastic spatial grains simulations a plurigaussian method is applied, which is based on the truncation of several standard Gaussian random functions. This approach is very flexible, since it allows to simultaneously manage the proportions of each grain category in a very general manner and to rigorously handle their spatial dependency relationships in the case of two or more grain categories. The obtained results show that the stochastically simulated porous media using the plurigaussian method adequately reproduces the proportions, basic statistics and sizes of the pore structures present in the studied reference images.     

核磁共振测井在火成岩地层应用的适应性分析

火成岩岩石具有高磁化率特征,与沉积岩差别明显,岩石的高磁化率会对核磁共振信号产生显著影响,开展核磁共振测井在火成岩地层应用的适应性分析研究,为广泛使用核磁共振测井用于火成岩储层评价提供参考.采用理论模拟、实验分析及实际测井资料相结合的方法,分析了高磁化率岩石的核磁共振响应特征.分析结果表明,火成岩岩石具有很高的磁化率,从酸性火成岩到基性火城岩,岩石的磁化率一般是逐渐增大的.高磁化率岩石孔隙内部会产生强梯度磁场,孔隙内部的磁场梯度越强,核磁共振的T2谱前移越明显,核磁信号衰减幅度也越大,核磁分析孔隙度与常规分析的孔隙度误差也越大;相同岩石磁化率情况下,岩石孔径越小,岩石孔隙内部磁场梯度越强,核磁信号衰减越大,核磁共振测井计算的孔隙度也越低.因此,核磁共振测井与岩性有关系,核磁共振测井会受到高磁化率岩石的显著影响.核磁共振测井在部分火成岩,尤其在中基性火成岩和小孔径火成岩储层中应用具有很大的局限性.     

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.     

Fundamental Changes in In Situ Air Sparging How Patterns

Two types of gas-phase flow patterns have been discussed and observed in the in situ air sparging (ISAS) literature: bubble flow and air channels. A critical factor affecting the flow pattern at a given location is the grain size of the porous medium. Visualization experiments reported in the literature indicate that a change in the flow pattern occurs around 1 to 2 mm grain diameters, with air channels occurring below the transition size and bubbles above. Analysis of capillary and buoyancy forces suggests that for a given gas-liquid-solid system, there is a critical size that dictates the dominant force, and the dominant force will in turn dictate the flow pattern. The dominant forces, and consequently the two-phase flow patterns, were characterized using a Bond number modified with the porous media aspect ratio (pore throat to pore body ratio). Laboratory experiments were conducted to observe flow patterns as a function of porous media size and air flow rate. The experimental results and the modified Bond number analysis support the relationship of flow patterns to grain size reported in the literature.     

天然气水合物和游离气饱和度估算的影响因素

讨论了不同水合物胶结类型的流体饱和多孔隙固体中地震波的衰减情况,分析了估算天然气水合物和游离气饱和度影响因素.结果表明, 地层孔隙度、纵波速度模型和弹性模量的计算方法是影响反演水合物和游离气饱和度的关键因素.含水合物地层的吸收与水合物胶结类型密切相关,当水合物远离固体颗粒,像流体一样充填在孔隙时,品质因子出现负异常,而当水合物胶结固体颗粒影响骨架的弹性性质,其品质因子出现正异常.根据布莱克海台地区164航次995井的测井资料,分别应用低频和高频速度模型估算了水合物和游离气饱和度.由低频速度模型得到的水合物饱和度(占孔隙空间的)10%～20%,游离气饱和度(占孔隙空间的)05%～1%;而由高频速度模型得到的水合物饱和度(占孔隙空间的)5%～10%,游离气饱和度(占孔隙空间的)1%～2%.     

Extraction of physically realistic pore network properties from three-dimensional synchrotron X-ray microtomography images of unconsolidated porous media systems

This paper presents application of a series of algorithms used to extract pore network structure from high-resolution three-dimensional synchrotron microtomography images of unconsolidated porous media systems. These algorithms are based on the three-dimensional skeletonization that simplifies the pore space to networks in the form of nodes connected to paths. Dilation algorithms were developed to generate inscribed spheres on the nodes and paths of the medial axis to represent pore-bodies and pore-throats of the network, respectively. The end result is a physically representative pore network structure, i.e. three-dimensional spatial distribution (i.e. x-, y-, and z-coordinates) of pore-bodies and pore-throats, pore-body size distribution, pore-throat size distribution, and the connectivity. Systems analyzed in this study include different glass bead systems and natural marine sand. The media ranged in size from 0.123 to 1.0 mm, while the image volumes ranged between 7.7 and 108.9 mm³. In addition to extracting the pore network structure, the porosity, specific surface area, and representative elementary volume analysis on the porosity were calculated. Spatial correlation between pore-body sizes in the network was investigated using semivariograms and integral scale concepts. The impact of resolution on the calculated property was also investigated.

In this work, we show that microtomography is an effective tool to non-destructively extract the structure of many systems. The quality of the datasets depends on photon energy, photon flux, size of the sample, type of the sample, and size of the sample ‘features’. Results show that the developed method of extracting pore network structure is applicable to ideal and natural porous media systems. The impact of resolution on the quantification of the network structure properties varies in its significance based on feature size of the system and the properties being calculated. Therefore, a thorough resolution sensitivity analysis should be carried out to determine the degree of error associated with a system imaged at a given resolution.     

岩石物理的理论模拟和数值实验新方法

当代物理实验科学和计算机科学技术的巨大进步为岩石物理的理论和实验研究开辟了新的领域.在细胞自动机基础上发展起来的格子气自动机和格子玻尔滋曼方法就是这种技术进步的产物.本文讨论了格子气自动机的发展及其应用于研究多孔岩石微观孔隙结构对宏观导电特性影响的新方法. 我们开发的模拟多孔岩石导电特性的数值实验新方法，提供了一种可深入到从微观孔隙结构这个尺度上来考察具有复杂孔隙结构的，孔隙度小于10%的低孔、低渗岩石的宏观导电特性及其影响因素.研究表明:Archie 系数m,n并不是传统上的意义，研究各种不同条件下F-、I-Sw关系，结果显示非阿尔奇现象与孔隙介质中孔隙、骨架和流体的混合导电网络有关，得出新的饱和度计算公式.同时还研究了泥质含量和分布、电阻率各向异性对宏观导电特性的影响，提出适用于电阻率各向异性地层的F-、I-Sw的关系.本文最后探讨了应用格子气自动机和格子玻尔滋曼方法进行岩心渗流和核磁共振数值实验的新方法及其发展前景.     

The influence of local fluid flow and the microstructure on elastic and anelastic rock properties

The frequency dependent mechanism of local fluid flow was found to be the decisive absorption and dispersion mechanism in fluid containing sandstones. In the ultrasonic frequency range local fluid flow and grain surface effects control the behaviour of highly porous and highly permeable rock if a pore fluid is present. Both mechanisms depend less on macroscopic rock parameters like porosity and permeability than essentially on microscopic parameters like crack size, crack density and grain contact properties. To demonstrate directly the important influence of the microstructure on the rock elastic and anelastic properties the microstructure of a sandstone was artificially changed by thermal cracking. The cracked rock exhibits a clearly changed behaviour at low uniaxial as well as at high hydrostatic pressure despite small changes of porosity and permeability. Fluid effects increase due to cracking. The experimental results are explained by means of a rock, model and local fluid flow. These results emphasize that it is the microstructure which controls the elastic and anelastic rock behaviour, even at high hydrostatic pressure.