Permeability Evolution During Non-linear Viscous Creep of Calcite Rocks

Permeability, storage capacity and volumetric strain were measured in situ during deformation of hot-pressed calcite aggregates containing 10, 20, and 30 wt% quartz. Both isostatic and conventional triaxial loading conditions were used. The tests were performed at confining pressure of 300 MPa, pore pressures between 50 to 290 MPa, temperatures from 673 to 873 K and strain rates of 3 × 10⁻⁵ s⁻¹. Argon gas was used as the pore fluid. The initial porosities of the starting samples varied from 5% to 9%, with higher porosity correlated to higher quartz content. Microstructural observations after the experiment indicate two kinds of pores are present: 1) Angular, crack-like pores along boundaries between quartz grains or between quartz and calcite grains and 2) equant and tubular voids within the calcite matrix. Under isostatic loading conditions, the compaction rate covaries with porosity and increases with increasing effective pressure. Most of the permeability reduction induced during compaction is irreversible and probably owes to plastic processes. As has been found in previous studies on hot-pressed calcite aggregates, permeability, k, is nonlinearly related to porosity, ϕ. Over small changes in porosity, the two parameters are approximately related as k ∝ ϕⁿ. The exponent n strongly increases as porosity decreases to a finite value (from about 4 to 6% depending on quartz content), suggesting a porosity percolation threshold. When subjected to triaxial deformation, the calcite-quartz aggregates exhibit shear-enhanced compaction, but permeability does not decrease as rapidly as it does under isostatic conditions. During triaxial compaction the exponent n only varies between 2 and 3. Non-isostatic deformation seems to reduce the percolation threshold, and, in fact, enhances the permeability relative to that at the same porosity during isostatic compaction. Our data provide constraints on the governing parameters of the compaction theory which describes fluid flow through a viscous matrix, and may have important implications for expulsion of sedimentary fluids, for fluid flow during deformation and metamorphism, and melt extraction from partially molten rocks.     

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.

     

Study of the Reservoir Damage during Cyclic Injection and Extraction Process in the Hutubi Gas Storage

During the injection and extraction process in gas storage,cyclic loading stress is applied to the reservoir pore structure,affecting the capacity and service life of gas storage. To study the influence of cyclic injection and extraction on reservoir physical property,a finite-element model of reservoir elastoplastic damage under the effect of pore pressure is established based on elastoplastic mechanics and fatigue-damage mechanics. Considering the mechanical property of the Hutubi reservoir and the injection-extraction mode of gas storage,the finite-element model is used to study the pore pressure and porosity change,fault safety,and ground surface deformation. The results show that the change in pore pressure and porosity,the deformation of the Hutubi fault,as well as the uplift and sink of the grounds surface are controlled by the fatigue damage of the reservoir pore structure during the injection-extraction process. After a 6-year service life, the cumulative deformation of the reservoir pore reaches its limit,causing pore structure collapse and porosity decrease. As a result,storage capacity declines and the ground surface starts to sink. Through this study,the safety of the Hutubi gas storage is evaluated,and some suggestions for field operations are offered.     

Permeability-porosity Relationships in Rocks Subjected to Various Evolution Processes

— It is well known that there is no “universal” permeability-porosity relationship valid in all porous media. However, the evolution of permeability and porosity in rocks can be constrained provided that the processes changing the pore space are known. In this paper, we review observations of the relationship between permeability and porosity during rock evolution and interpret them in terms of creation/destruction of effectively and non-effectively conducting pore space. We focus on laboratory processes, namely, plastic compaction of aggregates, elastic-brittle deformation of granular rocks, dilatant and thermal microcracking of dense rocks, chemically driven processes, as a way to approach naturally occurring geological processes. In particular, the chemically driven processes and their corresponding evolution permeability-porosity relationships are discussed in relation to sedimentary rocks diagenesis.     

Compaction and Failure in High Porosity Carbonates: Mechanical Data and Microstructural Observations

We investigated systematically the micromechanics of compaction in two carbonates of porosity above 30%, Majella grainstone and Saint Maximin limestone. The composition, grain size and pore surface area of these rocks were determined. Hydrostatic compression experiments were performed under dry and wet conditions beyond the onset of grain crushing. A significant water weakening effect was observed in both rocks. A set of conventional triaxial experiments was also performed on both rocks under dry conditions at confining pressures ranging from 3 to 31 MPa. Microstructural observations were carried out on the deformed samples. The mechanical behavior of these high porosity carbonates is dominated by shear-enhanced compaction associated in most cases with strain hardening. Stress-induced cracking and grain crushing are the dominant micromechanisms of deformation in both rocks. In Majella grainstone, compactive shear bands appeared at low confinement, in qualitative agreement with the deformation bands observed in the field. At higher confining pressures, compaction localization was inhibited and homogeneous cataclastic flow developed. In Saint Maximin limestone, compaction localization was observed at all confining pressures. An increasing number of compactive shear bands at various orientations appeared with increasing strain. These new data suggest that compaction localization is important in the mechanical compaction of high porosity carbonates.     

Dynamics of deformation and water flow in heterogeneous porous media and its impact on soil properties

The interaction of geomechanics and flow within a soil body induces deformation and pore pressure change. Deformation may change hydrogeological and elastic properties, which alters the mechanical behaviour and results in non‐linearity. To investigate this interaction effect in a heterogeneous porous medium, a stochastic poroelastic model is proposed. Monte Carlo simulations are performed to determine the mean and uncertainty of the parameter changes, displacement, and change in pore water pressure. Hydraulic conductivity is treated as the only random variable in the coupled geomechanics‐flow system due to its large variation compared to other mechanical and hydrogeological properties in natural environments. The three considered non‐linear models for the interaction between parameters and deformation are those that consider (1) porosity and hydraulic conductivity; (2) porosity and Young's modulus; and (3) a combined effect that includes porosity, hydraulic conductivity, and Young's modulus. Boundary effects on the coupled system are also explored. The relationships between changes of porosity, hydraulic conductivity, and Young's modulus are analytically shown to be non‐linear. Among the considered parameters, the deformation effect induces the largest reduction in hydraulic conductivity. The deformation‐induced change in hydraulic conductivity shows the most significant effect on the mean and variance of the change in pore water pressure and displacement, while changes in Young's modulus have the least effect. When the deformation effect is considered, the superposition relationship does not exist in the mean displacement and mean change in pore water pressure for the three scenarios considered; it exists for the case without deformation effects. Deformation also causes a reduction in the effective hydraulic conductivity for the whole domain. The scenario that considers both loading and discharge boundaries has larger changes in hydrogeological and geo‐mechanical parameters than those in scenarios that consider loading and discharge boundaries separately. The results indicate that the interaction between deformation and changes in parameters has a profound effect on the poroelastic system. The effect of deformation should thus be considered in modelling and practice. Copyright © 2009 John Wiley & Sons, Ltd.     

基于统计岩石物理模型的各向异性页岩储层参数反演

提出了各向异性页岩储层统计岩石物理反演方法.通过统计岩石物理模型建立储层物性参数与弹性参数的定量关系,使用测井数据及井中岩石物理反演结果作为先验信息,将地震阻抗数据定量解释为储层物性参数、各向异性参数的空间分布.反演过程在贝叶斯框架下求得储层参数的后验概率密度函数,并从中得到参数的最优估计值及其不确定性的定量描述.在此过程中综合考虑了岩石物理模型对复杂地下介质的描述偏差和地震数据中噪声对反演不确定性的影响.在求取最大后验概率过程中使用模拟退火优化粒子群算法以提高收敛速度和计算准确性.将统计岩石物理技术应用于龙马溪组页岩气储层,得到储层泥质含量、压实指数、孔隙度、裂缝密度等物性,以及各向异性参数的空间分布及相应的不确定性估计,为页岩气储层的定量描述提供依据.

     

Quantification of Exhumation from Sonic Velocity Data, Cooper Basin, Australia, and Implications for Hydrocarbon Exploration

Exhumation (defined as rock uplift minus surface uplift) in the Cooper Basin of South Australia and Queensland has been quantified using the compaction methodology. The sonic log, which is strongly controlled by the amount of porosity, is an appropriate indicator of compaction, and hence is used for quantifying exhumation from compaction. The traditional way of estimating exhumation based on the degree of overcompaction of a single shale unit has been modified and five units ranging in age from Permian to Triassic have been analysed. The results reveal that exhumation increases eastwards from the South Australia into the Queensland sector of the basin. The results show that exhumation in Late Triassic – Early Jurassic times, after the Cooper Basin deposition, seems to be 200–400 m higher than exhumation in Late Cretaceous – Tertiary times, after the Eromanga Basin deposition. This study has major implications for hydrocarbon exploration. Maturation of source rocks will be greater for any given geothermal history if exhumation is incorporated in maturation modelling. Exhumation values can also be used to improve porosity predictions of reservoir units in undrilled targets.     

成岩过程对五峰-龙马溪组页岩地震岩石物理特征的影响

五峰-龙马溪组页岩是目前国内页岩气勘探的首选层位,而其地震岩石物理特征是利用地震方法进行"甜点"预测的重要基础之一,但对五峰-龙马溪组页岩地震弹性特征变化规律的研究并未考虑沉积、成岩过程的影响,致使相应的规律性认识缺乏地质意义.在对五峰-龙马溪组页岩样品系统声学测量基础上,分析了页岩样品地震弹性性质的变化规律.利用X射线衍射分析、扫描电镜（SEM）、阴极发光（CL）与能谱分析确定了五峰-龙马溪组页岩在不同沉积环境下的成岩过程,并讨论了成岩过程与地震弹性性质变化规律的因果关系.研究结果表明,页岩中有机质（TOC）受高热演化程度的影响,其密度通常高于1.4 g·cm^-3,并接近于有机碳密度上限1.6 g·cm^-3（石墨密度）.五峰-龙马溪组页岩地震弹性性质变化规律整体受沉积环境控制,沉积环境的差异形成不同的成岩过程,致使地震弹性特征也表现出不同的变化规律.表现在五峰-龙马溪页岩样品动态岩石物理特征主要受岩石结构控制（支撑颗粒弹性性质）,而孔隙度、TOC含量以及孔隙形状则为对地震弹性特征影响的次一级因素.五峰-龙马溪组页岩上段为浅水陆棚相,机械压实与化学压实（硅质胶结）为先后两个过程,造成样品表现出高的速度-孔隙度变化率、高速度比（泊松比）、高各向异性以及低TOC含量的特征.五峰-龙马溪组页岩下段为深水陆棚相,机械压实过程中同时伴有生物成因的硅质胶结,造成岩石样品表现出较高TOC含量与孔隙度、各向异性较弱以及较小的速度-孔隙度变化率.研究结果可为五峰-龙马溪页气储层的测井解释和地震"甜点"预测提供依据.     

基于固体替换模型的有机质含量对页岩弹性性质的影响分析

页岩中的TOC（Total Organic Carbon,总有机碳）含量,对页岩的有效弹性模量以及与之相关的弹性波速度（P波和S波）有重要影响,建立弹性模量与TOC含量关系是页岩气甜点预测的重要手段之一.C&;S和S&;M两种固体置换理论主要针对孔隙度较大的砂岩,能否适用于孔隙度低、孔隙形态复杂和非均质性强的页岩目前尚未深入研究.鉴于目前已知的富有机质页岩的TOC赋存形态与裂缝以及孔隙形态类似,有关TOC含量对岩石弹性模量的影响可视为孔隙物质充填问题来研究.本文利用数字岩心技术,构造同一数字岩心不同TOC含量的样本群,基于C&;S和S&;M两种固体替换理论模型,通过有限元（FEM）数值模拟交叉验证,详细研究了两种固体替换方程对页岩的适用性和TOC含量对页岩弹性性质的影响.研究表明,由于实际岩心孔隙及TOC分布的非均质性,C&;S替换方程弹性模量预测值与FEM模拟结果存在差异,而S&;M替换方程预测值与FEM模拟结果基本一致,两种方程的预测差异揭示页岩非均质强度,利用S&;M替换方程中的参数α₁,α₂,β₁和β₂可详细分析实际岩心孔隙及TOC分布的非均质特征.

     

横观各向同性页岩岩石物理模型建立——以龙马溪组页岩为例

在龙马溪页岩微观物性特征分析的基础上,综合利用测井解释、微观测试分析资料,建立了一种适用于龙马溪页岩的横观各向同性岩石物理模型,该模型建模过程：将各向异性SCA和DEM模型联合模拟得到的黏土和干酪根混合物作为背景介质;采用SCA模型对脆性矿物混合物进行模拟,利用各向异性DEM将脆性矿物混合物添加到背景介质;进一步将空孔隙添加到页岩基质,并利用Brown-Korringa模型进行各向异性条件下的流体替换,从而得到横观各向同性页岩岩石物理模型.通过对四川盆地A井龙马溪页岩进行岩石物理建模分析,计算了孔隙纵横比、纵横波速、各向异性系数和弹性参数,检验了模型的准确性.研究结果表明：矿物颗粒和孔隙纵横比是影响模型精度的关键参数,黏土和干酪根颗粒纵横比为0.05,图像识别获得的脆性矿物颗粒纵横比主要分布于0.45~1.0（集中分布于0.5~0.85）,横波波速反演获得的孔隙纵横比主要分布于0.1~0.3（平均值约为0.22）;模型预测和实测纵波波速之间误差为-2.40%~2.21%（平均绝对误差仅1.20%）,预测和实测横波波速之间误差为-1.93%~1.42%（平均绝对误差仅0.64%）,证实了本文模型的准确性和精度.本文模型能够准确计算页岩5个独立的刚度系数,为页岩弹性参数、声波波速、各向异性和脆性分析提供了有效手段,也为后续地球物理和工程地质参数分析提供了重要依据.     

横观各向同性页岩岩石物理模型建立——以龙马溪组页岩为例

在龙马溪页岩微观物性特征分析的基础上,综合利用测井解释、微观测试分析资料,建立了一种适用于龙马溪页岩的横观各向同性岩石物理模型,该模型建模过程：将各向异性SCA和DEM模型联合模拟得到的黏土和干酪根混合物作为背景介质;采用SCA模型对脆性矿物混合物进行模拟,利用各向异性DEM将脆性矿物混合物添加到背景介质;进一步将空孔隙添加到页岩基质,并利用Brown-Korringa模型进行各向异性条件下的流体替换,从而得到横观各向同性页岩岩石物理模型.通过对四川盆地A井龙马溪页岩进行岩石物理建模分析,计算了孔隙纵横比、纵横波速、各向异性系数和弹性参数,检验了模型的准确性.研究结果表明：矿物颗粒和孔隙纵横比是影响模型精度的关键参数,黏土和干酪根颗粒纵横比为0.05,图像识别获得的脆性矿物颗粒纵横比主要分布于0.45~1.0（集中分布于0.5~0.85）,横波波速反演获得的孔隙纵横比主要分布于0.1~0.3（平均值约为0.22）;模型预测和实测纵波波速之间误差为-2.40%~2.21%（平均绝对误差仅1.20%）,预测和实测横波波速之间误差为-1.93%~1.42%（平均绝对误差仅0.64%）,证实了本文模型的准确性和精度.本文模型能够准确计算页岩5个独立的刚度系数,为页岩弹性参数、声波波速、各向异性和脆性分析提供了有效手段,也为后续地球物理和工程地质参数分析提供了重要依据.

     

Using synchrotron X-ray microtomography to characterize the pore network of reservoir rocks: A case study on carbonates

In this work we propose a new methodology to calculate pore connectivity in granular rocks. This method is useful to characterize the pore networks of natural and laboratory compaction bands (CBs), and compare them with the host rock pore network.Data were collected using the synchrotron X-ray microtomography technique and quantitative analyses were carried out using the Pore3D software library. The porosity was calculated from segmented tridimensional images of deformed and pristine rocks. A process of skeletonization of the pore space was used to obtain the number of connected pores within the rock volume. By analyzing the skeletons the differences between natural and laboratory CBs were highlighted. The natural CB has a lower porosity than to the laboratory one. In natural CBs, the grain contacts appear welded, whereas laboratory CBs show irregular pore shape. Moreover, we assessed for the first time how pore connectivity evolves as a function of deformation, documenting the mechanism responsible for pore connectivity drop within the CBs.     

基于双相介质理论的储层参数反演方法

传统基于单相介质理论的储层参数反演方法将孔隙流体与固体骨架等效为单一固体,弱化了孔隙流体的影响,反演结果精度不高. 本文提出根据双相介质理论反演储层参数的方法. 首先,在前人研究的基础上,利用岩石物理模型建立弹性参数与孔隙度、饱和度、泥质含量等储层参数间的关系,进而将双相介质反射系数推导为储层参数的函数;其次,根据贝叶斯反演理论,在高斯噪声假设的基础上,采用更加符合实际情况的修正柯西分布函数描述反射系数的稀疏性,推导出储层物性参数目标反演函数;最后, 应用差分进化非线性全局寻优算法来求解目标反演函数,使得反演结果与实际资料间误差最小. 新方法旨在突出流体对介质反射系数的影响,以期得到较高的储层参数反演精度. 模型与实际资料测试均表明该方法可行、有效且反演精度较高.     

泥页岩岩石物理建模研究

泥页岩由于其复杂的岩石特性（主要是裂缝及有机质的存在）,目前还没有有效的岩石物理模型可以较为精确的模拟其性质.本文在自洽模型和微分等效介质模型的基础上,引入Berryman三维孔隙形态及Brown-Korringa固体替代技术,建立适用于富有机质泥页岩的新型岩石物理模型.在此基础上进行正演分析,讨论不同孔隙形态对于自洽模型的临界孔隙度以及岩石速度的影响.正演分析的结果表明即使将未知的混合岩石作为背景岩石,微分有效介质模型的引入使得固体相和流体相仍然不是对称的,临界孔隙度不一定要落在0.4到0.6之间.且不同的孔隙形状对于自洽模型的临界孔隙度以及岩石的速度具有明显的影响.此外,基于岩石物理模型,文章讨论了不同孔隙形态、不同泥质含量时有机质对于岩石弹性性质的影响.最后利用一口页岩气井对该模型进行验证,预测的纵横波速度与测井结果吻合的很好,证明了该模型对于富有机质泥页岩的适用性.     

基于多弹簧模型的钢框架结构三维弹塑性地震反应分析

文章提出了考虑剪切变形弹塑性刚度影响的多弹簧模型的空间梁柱单元,用于反复加载下钢构件的数值模拟。应用多轴应力状态下的塑性应力-应变关系理论,在单元模型中考虑了弹塑性区域剪切变形对单元的弹塑性刚度的影响,针对单元模型的塑性区长度和弹簧布置两个参数,文中给出了合理建议取值。数值模拟分析表明,所提出的单元模型能够很好地模拟钢构件的弹塑性性能。在此基础上,以多高层钢结构商业设计软件MTS为平台,进行三维钢框架结构弹塑性动力时程分析模块的开发。最后,文章对一纯钢框架结构足尺振动台试验进行数值模拟,模拟分析结果表明,本文所提出的多弹簧单元模型及开发的动力分析模块能够较好地模拟钢结构在地震作用下的弹塑性性能。     

Acoustic Emissions Monitoring during Inelastic Deformation of Porous Sandstone: Comparison of Three Modes of Deformation

In some reservoirs, large deformations can occur during oil or gas production because of the effective stress change. For very porous rocks, these production operations can be sufficient to cause inelastic deformation and irreversible damage. Rock formations can undergo deformation by different mechanisms, including dilatancy or pore collapse. In the laboratory, it has been shown that the inelastic deformation and failure mode of porous rocks are pressure sensitive. Indeed, when subjected to an overall compressive loading, a porous rock may fail by shear localization, compaction localization, or by cataclastic compaction. Acoustic emission (AE) records provide important information to understand the failure mode of rocks: the spatial evolution of damage as well as the source mechanisms can be followed using this technique. In this paper, we present three different laboratory axisymmetric compression experiments, performed on Bleurswiller sandstone, which enable us to compare the acoustic emission signature of these three modes of deformation. Our data show that compaction localization and cataclastic compaction are characterized by similar acoustic signatures (in terms of AE sources characteristics and evolution of AE number), in comparison to the acoustic signature from shear localization. This implies similar micromechanisms involved during compaction bands formation and cataclastic compaction.     

基于InSAR数据分析四川盆地南部长宁页岩气区块地表形变场基本特征

近年来随着我国页岩气大规模开采,四川盆地南部活动构造相对稳定的地区出现了一系列微震和有感地震,甚至是破坏性地震。这些地震是否为工业开采所诱发,目前已有研究从时空相关性给出了一些统计推断,本文则从形变观测角度分析页岩气开采能否产生可以检测到的地面形变,以揭示形变信息与页岩气开采的关系,尝试为页岩气开采提供有效的监测手段。基于长波ALOS-2卫星雷达数据对长宁页岩气区块近两三年内的InSAR地表形变展开探测,检测页岩气发活跃时段内的形变时间序列信息。结果显示：考虑到不同观测砽技縂术的误差水平和观测角度差异,两种卫星数据均反映了一致的地表形变分布,且形变场与页岩气开采井的空间分布有很好的对应关系;压裂注液过程会造成地表快速隆升,生产过程中随着流体扩散地表会出现沉降和水平运动,初步揭示出页岩气生产过程中地面形变的非稳态变形特征。这表明在四川盆地南部复杂的形变观测条件下,InSAR技术是页岩气开采有效的监测手段,能够弥补地震学观测的不足。     

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.     

Constraints on velocity-depth trends from rock physics models

Estimates of depth, overpressure and amount of exhumation based on sonic data for a sedimentary formation rely on identification of a normal velocity–depth trend for the formation. Such trends describe how sonic velocity increases with depth in relatively homogeneous, brine‐saturated sedimentary formations as porosity is reduced during normal compaction (mechanical and chemical). Compaction is ‘normal’ when the fluid pressure is hydrostatic and the thickness of the overburden has not been reduced by exhumation. We suggest that normal porosity at the surface for a given lithology should be constrained by its critical porosity, i.e. the porosity limit above which a particular sediment exists only as a suspension. Consequently, normal velocity at the surface of unconsolidated sediments saturated with brine approaches the velocity of the sediment in suspension. Furthermore, porosity must approach zero at infinite depth, so the velocity approaches the matrix velocity of the rock and the velocity–depth gradient approaches zero. For sediments with initially good grain contact (when porosity is just below the critical porosity), the velocity gradient decreases with depth. By contrast, initially compliant sediments may have a maximum velocity gradient at some depth if we assume that porosity decreases exponentially with depth. We have used published velocity–porosity–depth relationships to formulate normal velocity–depth trends for consolidated sandstone with varying clay content and for marine shale dominated by smectite/illite. The first relationship is based on a modified Voigt trend (porosity scaled by critical porosity) and the second is based on a modified time‐average equation. Baselines for sandstone and shale in the North Sea agree with the established constraints and the shale trend can be applied to predict overpressure. A normal velocity–depth trend for a formation cannot be expressed from an arbitrary choice of mathematical functions and regression parameters, but should be considered as a physical model linked to the velocity–porosity transforms developed in rock physics.