Velocities of compressional and shear waves in limestones

Carbonate rocks are important hydrocarbon reservoir rocks with complex textures and petrophysical properties (porosity and permeability) mainly resulting from various diagenetic processes (compaction, dissolution, precipitation, cementation, etc.). These complexities make prediction of reservoir characteristics (e.g. porosity and permeability) from their seismic properties very difficult. To explore the relationship between the seismic, petrophysical and geological properties, ultrasonic compressional‐ and shear‐wave velocity measurements were made under a simulated in situ condition of pressure (50 MPa hydrostatic effective pressure) at frequencies of approximately 0.85 MHz and 0.7 MHz, respectively, using a pulse‐echo method. The measurements were made both in vacuum‐dry and fully saturated conditions in oolitic limestones of the Great Oolite Formation of southern England. Some of the rocks were fully saturated with oil. The acoustic measurements were supplemented by porosity and permeability measurements, petrological and pore geometry studies of resin‐impregnated polished thin sections, X‐ray diffraction analyses and scanning electron microscope studies to investigate submicroscopic textures and micropores. It is shown that the compressional‐ and shear‐wave velocities (V_p and V_s, respectively) decrease with increasing porosity and that V_p decreases approximately twice as fast as V_s. The systematic differences in pore structures (e.g. the aspect ratio) of the limestones produce large residuals in the velocity versus porosity relationship. It is demonstrated that the velocity versus porosity relationship can be improved by removing the pore‐structure‐dependent variations from the residuals. The introduction of water into the pore space decreases the shear moduli of the rocks by about 2 GPa, suggesting that there exists a fluid/matrix interaction at grain contacts, which reduces the rigidity. The predicted Biot–Gassmann velocity values are greater than the measured velocity values due to the rock–fluid interaction. This is not accounted for in the Biot–Gassmann velocity models and velocity dispersion due to a local flow mechanism. The velocities predicted by the Raymer and time‐average relationships overestimated the measured velocities even more than the Biot model.     

岩石物理弹性参数规律研究

根据辽东湾凹陷某区在地层条件和不同流体相态(气饱和、水饱和等)下岩石纵波速度、横波速度及密度等岩心测试数据,以及岩石矿物成分、孔隙度等常规岩心分析数据,统计分析了岩石弹性参数变化规律.采用有效流体模型、斑块饱和模型进行了纵、横波速度理论计算,并和实验测量结果比较,认为高孔、高渗岩石可以看作有效流体模型,低孔、低渗岩石更接近斑块饱和模型.这些规律和认识对于指导储层预测和油气检测及地震振幅综合解释有重要的意义.     

岩石孔隙结构的地震信号特征

岩石孔隙结构是控制砂岩和碳酸盐岩的地震波速度和渗透率的重要参数之一。如果两种类似的岩石其孔隙度一定,而渗透率不同,那么它们的声波速度相差2km/s,而渗透率两者则可能相差近6个数量级,即从0.01mD到20mO。在本文中我们总结了由一个广义孔隙弹性理论简化的一个双参数弹性速度模型，以描述孔隙结构对弹性波的影响。由于矿物和储层的流体是给定的,我们用孔隙度和骨架的柔性(挠性)因子来确定速度模型,这个模型可以用于地震反演和储层表征,已改善孔隙度和储量的计算骨架柔性因子可用于岩石结构(PST)类型的定量分类,并可以利用叠前、叠后的两种地震资料将其与孔隙的连通性和渗透率联系起来。本项研究同时也有助于说明为什么振幅与偏移距(AVO)分析用于流体检测在某些情况下失败。这是由于孔隙结构对地震波的影响能够掩盖所有流体效应，特别是在碳酸岩中。     

Interrelations Between Thermal Conductivity and Other Physical Properties of Rocks: Experimental Data

— A new non-contact and non-destructive optical scanning instrument provided a large number of high-precision measurements of thermal conductivity tensor components in samples of sedimentary and impact rocks, as well as new insights into interrelations between thermal conductivity and other physical properties. More than 800 core samples (dry and fluid-saturated) of sedimentary rocks from different Russian oil-gas deposits and impact rocks from the well “Nördlingen 1973” drilled in the Ries impact structure (Germany) were studied using optical scanning technology. It was established that the thermal conductivity parallel to the stratification is more informative for petrophysical investigations than the thermal conductivity perpendicular to the layering. Different approaches were developed to estimate porosity, permeability, pore space geometry, and matrix thermal conductivity with a combination of thermal conductivity measurements in dry and fluid-saturated samples and mathematical modelling. These approaches allow prediction of the rock porosity and permeability and their spatial distribution along a well using thermal conductivity measurements performed with the optical scanning instrument directly applied to cores. Conditions and constraints for using Lichtenecker-Asaad's theoretical model for the estimation of porosity and thermal conductivity of sedimentary rocks were determined. A correlation between thermal conductivity and acoustic velocity, porosity, density, and electric resistivity of impact rocks was found for different rock types. New relationships between permeability, electrical and thermal conductivity found for sedimentary rocks are described.     

Permeability and degassing of dome lavas undergoing rapid decompression: An experimental determination

The gas permeability of volcanic rocks may influence various eruptive processes. The transition from a quiescent degassing dome to rock failure (fragmentation) may, for example, be controlled by the rocks permeability, in as much as it affects the speed by which a gas overpressure in vesicles is reduced in response to decompression. Using a modified shock-tube-based fragmentation bomb (Alidibirov and Dingwell 1996a,b; Spieler et al. 2003a), we have measured unsteady-state permeability at a high initial pressure differential. Following sudden decompression above the rock cylinder, pressurized gas flows through the sample. Two pressure transducers record the pressure signals above and below the sample. A transient 1D filtration code has been developed to calculate permeability using the experimental decay curve of the lower pressure transducer. Additionally an analytical steady-state method to achieve permeability is presented as an alternative to swiftly predict the sample permeability in a sufficiently precise manner. Over 100 permeability measurements have been performed on samples covering a wide range of porosity. The results show a general positive relationship between porosity and permeability with a high data scatter. Our preferred interpretation of the results is a combination of two different, but overlapping effects. We propose that at low porosities, gas escape occurs predominantly through microcracks or elongated micropores and therefore could be described by simplified forms of Kozeny–Carman relations (Carman 1956) and fracture flow models. At higher porosities, the influence of vesicles becomes progressively stronger as they form an increasingly connected network. Therefore, a model based on the percolation theory of fully penetrable spheres is used, as a first approximation, to describe the permeability-porosity trend. In the data acquired to date it is evident, that in addition to the porosity control, the samples bubble size, shape and distribution strongly influence the permeability. This leads to a range of permeability values up to 2.5 orders of magnitude at a given porosity.     

Mechanism for calcite dissolution and its contribution to development of reservoir porosity and permeability in the Kela 2 gas field,Tarim Basin,China

This study is undertaken to understand how calcite precipitation and dissolution contributes to depth-related changes in porosity and permeability of gas-bearing sandstone reservoirs in the Kela 2 gas field of the Tarim Basin, Northwestern China. Sandstone samples and pore water samples are col-lected from well KL201 in the Tarim Basin. Vertical profiles of porosity, permeability, pore water chem-istry, and the relative volume abundance of calcite/dolomite are constructed from 3600 to 4000 m below the ground surface within major oil and gas reservoir rocks. Porosity and permeability values are in-versely correlated with the calcite abundance, indicating that calcite dissolution and precipitation may be controlling porosity and permeability of the reservoir rocks. Pore water chemistry exhibits a sys-tematic variation from the Na2SO4 type at the shallow depth (3600-3630 m), to the NaHCO3 type at the intermediate depth (3630―3695 m),and to the CaCl2 type at the greater depth (3728―3938 m). The geochemical factors that control the calcite solubility include pH, temperature, pressure, Ca2 concen-tration, the total inorganic carbon concentration (ΣCO2), and the type of pore water. Thermodynamic phase equilibrium and mass conservation laws are applied to calculate the calcite saturation state as a function of a few key parameters. The model calculation illustrates that the calcite solubility is strongly dependent on the chemical composition of pore water, mainly the concentration difference between the total dissolved inorganic carbon and dissolved calcium concentration (i.e., [ΣCO2] -[Ca2 ]). In the Na2SO4 water at the shallow depth, this index is close to 0, pore water is near the calcite solubility. Calcite does not dissolve or precipitate in significant quantities. In the NaHCO3 water at the intermedi-ate depth, this index is greater than 0, and pore water is supersaturated with respect to calcite. Massive calcite precipitation was observed at this depth interval and this intensive cementation is responsible for decreased porosity and permeability. In the CaCl2 water at the greater depth, pore water is un-der-saturated with respect to calcite, resulting in dissolution of calcite cements, as consistent with microscopic dissolution features of the samples from this depth interval. Calcite dissolution results in formation of high secondary porosity and permeability, and is responsible for the superior quality of the reservoir rocks at this depth interval. These results illustrate the importance of pore water chemis-try in controlling carbonate precipitation/dissolution, which in turn controls porosity and permeability of oil and gas reservoir rocks in major sedimentary basins.     

The porosity trend and pore sizes of the rocks in the continental crust of the earth: Evidence from experimental data on permeability

The depth trends of permeability are constructed from the measurements of the tight rocks typical of the basement of the continental crust at temperatures up to 600°C and pressures up to 200 MPa. It is established that the permeability decreases with depth. The statistical processing of the experimental data yielded the generalized dependence logk = ?12.6-3.23H ^0.223. The method is suggested and, based on the experimental data on permeability, the estimates are obtained for the effective diameters of the pore channels and effective porosity at the PT parameters corresponding to the in situ deep zones of the continental crust. It is found that porosity decreases with depth, while distinct depth dependence of the pore sizes is not observed. The dependence of porosity on the depth is approximated by the relationship logφ = ?0.65–0.1H + 0.0019H ². The porosity is estimated at a few percent for a depth of 10 km with a decline to 0.01–0.1% at 35 km. The estimates of porosity retrieved from the experimental data agree with the theoretical calculations based on the present-day ideas of the structure of the discrete media and with the results of magnetotelluric sounding. Thus, according to three independent estimates, the porosity of the rocks of the continental crust decreases with depth. At the same time, in both the intermediate and lower crust there are intervals where the porosity values suggest the presence of fluid-saturated horizons at these depths.     

Effect and mechanism of stresses on rock permeability at different scales

1 Introduction Unlike general solids, rocks are porous materialswhich include different scales of pores, such as pores, cracks, fractures, capillary and disfigurement in the crystal, tiny pores and cracks between crystal grains at micro-scale, in which the fluid is water, oil or gas. Thedifferences between rocks and solids can be seen in two aspects, one is stresses bearing states. Solids are only subjected to external stresses, while rocks are subjected to external stresses σ ij (i, j=1,2,3)…     

汶川地震断裂带水岩相互作用及其对断裂带演化影响

汶川地震断层岩的矿物学和地球化学特征揭示出地震断层经历了漫长时间演化和复杂的水岩相互作用.间震期水岩相互作用导致断层岩中的破碎矿物蚀变,尤其是长石等矿物含量渐渐减少甚至消失,而黏土矿物（蒙脱石、伊利石、伊/蒙混层、绿泥石等）含量逐渐增高,以及如黄铁矿、石膏、重晶石、坡缕石等热液系统中常见的矿物大量出现;Mg、P、Ti、Mn、Fe等元素倾向富集在断层带中,而Si、K和Na等出现明显的亏损;元素的大量迁移导致断层带的体积巨量亏损.实验结果表明,黏土矿物的亲水性引起水渗透率比干燥气体渗透率明显偏低,并且二者偏差无法通过Klinkenberg校正消除.蒙脱石吸水膨胀和黏土矿物颗粒表面吸附孔隙流体造成孔隙度降低是导致水渗透率偏低的重要原因.断层岩碎屑结构使得其中的孔隙可能在600 MPa围压下得以保存,从而有助于流体沿断层带下渗,并在断层带深部形成高流体孔隙压.地震断层的主要矿物学及粒度分布特征并非在地震破裂过程中形成,因此利用断层岩粒度分布资料估算地震破裂能并不合适.     

裂缝-孔隙介质储层渗透率表征及其影响因素分析

含裂缝多孔介质渗透率预测是非常规油气资源勘探开发的一个紧迫问题.现有多孔介质岩石物理模型通常利用圆形孔管模拟宏观岩石孔隙空间,难以定量描述软孔隙/裂缝在压力作用下的闭合情况,缺乏裂缝/孔隙间流量交换的连通机制.本文提出含三维裂缝/软孔隙网络多孔介质模型,将储层岩石裂缝/软孔隙表示为椭圆截面微管,建立了周期性压力作用下微观裂缝流量表达式,通过网络模型和流量守恒条件,得到含有三维裂缝/软孔隙网络的多孔介质渗透率计算方法.数值算例表明,预测结果与实验数据分布范围吻合很好,能够给出不同类型岩心对应孔隙纵横比的分布图.三维裂缝/软孔隙网络模型建立了宏观可观测量与裂缝参数之间关系,能够定量分析岩石渗透率随裂缝体密度、纵横比、孔隙流体类型和围压等因素的变化规律,为复杂条件下储层渗透率预测提供了一种有效方法.     

Numerical estimation of carbonate rock properties using multiscale images

Characterizing the pore space of rock samples using three‐dimensional (3D) X‐ray computed tomography images is a crucial step in digital rock physics. Indeed, the quality of the pore network extracted has a high impact on the prediction of rock properties such as porosity, permeability and elastic moduli. In carbonate rocks, it is usually very difficult to find a single image resolution which fully captures the sample pore network because of the heterogeneities existing at different scales. Hence, to overcome this limitation a multiscale analysis of the pore space may be needed. In this paper, we present a method to estimate porosity and elastic properties of clean carbonate (without clay content) samples from 3D X‐ray microtomography images at multiple resolutions. We perform a three‐phase segmentation to separate grains, pores and unresolved porous phase using 19 μm resolution images of each core plug. Then, we use images with higher resolution (between 0.3 and 2 μm) of microplugs extracted from the core plug samples. These subsets of images are assumed to be representative of the unresolved phase. We estimate the porosity and elastic properties of each sample by extrapolating the microplug properties to the whole unresolved phase. In addition, we compute the absolute permeability using the lattice Boltzmann method on the microplug images due to the low resolution of the core plug images. In order to validate the results of the numerical simulations, we compare our results with available laboratory measurements at the core plug scale. Porosity average simulations for the eight samples agree within 13%. Permeability numerical predictions provide realistic values in the range of experimental data but with a higher relative error. Finally, elastic moduli show the highest disagreements, with simulation error values exceeding 150% for three samples.     

多孔可变临界孔隙度模型及储层孔隙结构表征

碳酸盐岩、致密砂岩和页岩等储层具有孔隙类型多样、孔隙结构复杂和非均质性强等特征,属于典型的多重孔隙储层,孔隙结构表征是多重孔隙储层预测和流体识别的关键.现有的孔隙结构表征方法大多利用孔隙纵横比或者构建一种新参数来描述孔隙结构.岩石临界孔隙度模型是一种常用的岩石物理模型,具有一定的物理意义和地质含义.本文推导了岩石临界孔隙度与岩石孔隙结构(孔隙纵横比)之间的关系,进而利用极化(形状)因子建立临界孔隙度与弹性参数之间的关系,构建了能够包含多种孔隙类型的多孔可变临界孔隙度模型.利用多孔可变临界孔隙度模型由储层的弹性参数反演不同孔隙类型的体积含量.实验室测量数据和实际测井数据表明,多孔可变临界孔隙度模型能够适用于多重孔隙储层岩石物理建模和孔隙结构表征.     

PHYSICAL PROPERTIES OF SYNTHETIC SANDSTONE ROCKS1

A novel process is used to coat glass spheres with a polymerizing thermo-setting resin, only microns thick. Synthetic rocks of known grain size distribution and pore space characteristics are then made by heating the resin-coated glass spheres under compression in a special mould. The dynamic Young's moduli of these rocks are found to be affected by the percentage of resin content (cement) and the synthetic diagenesis rather than the grain size and permeability.     

Laboratory measurement of compaction-induced permeability change in porous rocks: Implications for the generation and maintenance of pore pressure excess in the crust

Permeability exerts significant control over the development of pore pressure excess in the crust, and it is a physical quantity sensitively dependent on the pore structure and stress state. In many applications, the relation between permeability and effective mean stress is assumed to be exponential and that between permeability and porosity is assumed to be a power law, so that the pressure sensitivity of permeability is characterized by the coefficient and the porosity sensitivity by the exponent . In this study, we investigate experimentally the dependence of permeability on pressure and porosity in five sandstones with porosities ranging from 14% to 35% and we review published experimental data on intact rocks, unconsolidated materials and rock fractures. The laboratory data show that the pressure and porosity sensitivities differ significantly for different compaction mechanisms, but for a given compaction mechanism, the data can often be approximated by the empirical relations. The permeabilities of tight rocks and rock joints show relatively high pressure sensitivity and low porosity sensitivity. A wide range of values for and have been observed in relation to the mechanical compaction of porous rocks, sand and fault gouge, whereas the porosity sensitivity for chemical compaction processes is often observed to be given by 3. We show that since the ratio / corresponds to the pore compressibility, the different dependences of permeability on porosity and pressure are related to the pore structure and its compressibility. Guided by the laboratory data, we conduct numerical simulations on the development of pore pressure in crustal tectonic settings according to the models ofWalder andNur (1984) andRice (1992). Laboratory data suggest that the pressure sensitivity of fault gouge is relatively low, and to maintain pore pressure at close to the lithostatic value in the Rice model, a relatively high influx of fluid from below the seismogenic layer is necessary. The fluid may be injected as vertically propagating pressure pulses into the seismogenic system, andRice's (1992) critical condition for the existence of solitary wave is shown to be equivalent to >1, which is satisfied by most geologic materials in the laboratory. Laboratory data suggest that the porosity sensitivity is relatively high when the permeability is reduced by a coupled mechanical and chemical compaction process. This implies that in a crustal layer, pore pressure may be generated more efficiently than cases studied byWalder andNur (1984) who assumed a relatively low porosity sensitivity of =2.     

Rock physics modelling of porous rocks with multiple pore types: a multiple-porosity variable critical porosity model

A critical porosity model establishes the empirical relationship between a grain matrix and a dry rock by the concept of critical porosity. The model is simple and practical and widely used. But the critical porosity in the model is a fixed value that cannot relate to pore structure. The aim of this paper is to establish the theoretical relationship between critical porosity and pore structure by combining Kuster–Toksöz theory with the critical porosity model. Different from the traditional critical porosity model, critical porosity is not an empirical value but varied with pore shape and the ratio of bulk modulus versus shear modulus of the grain matrix. The substitution of the theoretical relationship into Kuster–Toksöz theory will generate the formulae for the bulk and shear moduli of multiple-porosity dry rocks, which is named the multiple-porosity variable critical porosity model. The new model has been used to predict elastic moduli for sandstone and carbonate rock. We compare the modelling results for P- and S-wave velocities and elastic moduli with the experimental data. The comparison shows that the new model can be used to describe the elastic properties for the rocks with multiple pore types.     

Quantitative geophysical pore‐type characterization and its geological implication in carbonate reservoirs

This paper discusses and addresses two questions in carbonate reservoir characterization: how to characterize pore‐type distribution quantitatively from well observations and seismic data based on geologic understanding of the reservoir and what geological implications stand behind the pore‐type distribution in carbonate reservoirs. To answer these questions, three geophysical pore types (reference pores, stiff pores and cracks) are defined to represent the average elastic effective properties of complex pore structures. The variability of elastic properties in carbonates can be quantified using a rock physics scheme associated with different volume fractions of geophysical pore types. We also explore the likely geological processes in carbonates based on the proposed rock physics template. The pore‐type inversion result from well log data fits well with the pore geometry revealed by a FMI log and core information. Furthermore, the S‐wave prediction based on the pore‐type inversion result also shows better agreement than the Greensberg‐Castagna relationship, suggesting the potential of this rock physics scheme to characterize the porosity heterogeneity in carbonate reservoirs. We also apply an inversion technique to quantitatively map the geophysical pore‐type distribution from a 2D seismic data set in a carbonate reservoir offshore Brazil. The spatial distributions of the geophysical pore type contain clues about the geological history that overprinted these rocks. Therefore, we analyse how the likely geological processes redistribute pore space of the reservoir rock from the initial depositional porosity and in turn how they impact the reservoir quality.     

CO2-induced dissolution of low permeability carbonates. Part II: Numerical modeling of experiments

We used the 3D continuum-scale reactive transport models to simulate eight core flood experiments for two different carbonate rocks. In these experiments the core samples were reacted with brines equilibrated with pCO₂ = 3, 2, 1, 0.5 MPa (Smith et al., 2013 [27]). The carbonate rocks were from specific Marly dolostone and Vuggy limestone flow units at the IEAGHG Weyburn-Midale CO₂ Monitoring and Storage Project in south-eastern Saskatchewan, Canada. Initial model porosity, permeability, mineral, and surface area distributions were constructed from micro tomography and microscopy characterization data. We constrained model reaction kinetics and porosity–permeability equations with the experimental data. The experimental data included time-dependent solution chemistry and differential pressure measured across the core, and the initial and final pore space and mineral distribution. Calibration of the model with the experimental data allowed investigation of effects of carbonate reactivity, flow velocity, effective permeability, and time on the development and consequences of stable and unstable dissolution fronts.The continuum scale model captured the evolution of distinct dissolution fronts that developed as a consequence of carbonate mineral dissolution and pore scale transport properties. The results show that initial heterogeneity and porosity contrast control the development of the dissolution fronts in these highly reactive systems. This finding is consistent with linear stability analysis and the known positive feedback between mineral dissolution and fluid flow in carbonate formations. Differences in the carbonate kinetic drivers resulting from the range of pCO₂ used in the experiments and the different proportions of more reactive calcite and less reactive dolomite contributed to the development of new pore space, but not to the type of dissolution fronts observed for the two different rock types. The development of the dissolution front was much more dependent on the physical heterogeneity of the carbonate rock. The observed stable dissolution fronts with small but visible dissolution fingers were a consequence of the clustering of a small percentage of larger pores in an otherwise homogeneous Marly dolostone. The observed wormholes in the heterogeneous Vuggy limestone initiated and developed in areas of greater porosity and permeability contrast, following pre-existing preferential flow paths.Model calibration of core flood experiments is one way to specifically constrain parameter input used for specific sites for larger scale simulations. Calibration of the governing rate equations and constants for Vuggy limestones showed that dissolution rate constants reasonably agree with published values. However the calcite dissolution rate constants fitted to the Marly dolostone experiments are much lower than those suggested by literature. The differences in fitted calcite rate constants between the two rock types reflect uncertainty associated with measured reactive surface area and appropriately scaling heterogeneous distribution of less abundant reactive minerals. Calibration of the power-law based porosity–permeability equations was sensitive to the overall heterogeneity of the cores. Stable dissolution fronts of the more homogeneous Marly dolostone could be fit with the exponent n = 3 consistent with the traditional Kozeny–Carman equation developed for porous sandstones. More impermeable and heterogeneous cores required larger n values (n = 6–8).     

Improved Interpretation of Nuclear Magnetic Resonance T1 and T2 Distributions for Permeability Prediction: Simulation of Diffusion Coupling for a Fractal Cluster of Pores

NMR relaxometry is a powerful tool for inferring porosity and permeability data. In practice, measured magnetization decay curves are inverted for relaxation time distributions. Subsequently, one presumes a linear relationship between the pore radius distribution and the T ₁ and T ₂ distribution, for longitudinal and transverse magnetization, respectively. The fundamental equations used are based on a pore model, in which pores are assumed to be isolated from each other with respect to the NMR process and have smooth walls. The present study is based on a geometrical pore space model with connected pores and structured pore walls. The physical processes of surface relaxation, irreversible dephasing of magnetic spins and diffusive proton exchange between pores, are described by a system of differential equations. The solution yields a set of exponential functions representing the relaxation time distribution. We describe the difference between the distributions obtained for diffusion coupling and for isolated pores. With diffusion coupling on, the spectral width of the T ₁ distribution is strongly reduced, which indicates that the influence of large and small radii according to the T ₁-pore radius relationship is mixed to some extent. For a fractal pore space structure, where large pores are surrounded by adjacent minor pores, the T ₁ distribution does not resolve these substructures. Nevertheless, permeability values calculated from the logarithmic mean relaxation time T _1,LM are quite the same for diffusion coupling and for isolated pores. The T ₂ distribution for diffusion coupling is little constricted and gives a better resolution of the pore wall structures than the corresponding T ₁ distribution. The permeability values from T ₂ distributions agree with the values from longitudinal magnetization, provided that we use a corrected relaxation time T _2,corr, accounting for the dependence of the surface relaxivity ρ ₂ on pore radius. The study shows that radius distributions calculated from a T ₁ and from a T ₂ distribution differ from one another and both present an altered image of the true pore radius distribution. In practice, this has no serious influence on estimating permeability of medium- to high-permeability sandstones with the currently applied methods. The presented methodology of calculating the NMR response of pore space models with diffusion coupling may facilitate understanding porosity-permeability relationships of different rock types such as carbonate rocks with micro-porosity.     

Analysis of laboratory data on ultrasonic monitoring of permeability reduction due to biopolymer formation in unconsolidated granular media

We show how to estimate the fluid permeability changes due to accumulated biopolymer within the pore space of a granular material using laboratory measurements of overall permeability, together with various well‐known quantitative measures (e.g., porosity, specific surface area, and formation factor) of the granular medium microstructure. The main focus of the paper is on mutual validation of existing theory and a synthesis of new experimental results. We find that the theory and data are in good agreement within normal experimental uncertainties. We also establish quantitative empirical relationships between seismic and/or acoustic attenuation and overall permeability for these same systems.