Constructing a discrete fracture network constrained by seismic inversion data

Rock fractures are of great practical importance to petroleum reservoir engineering because they provide pathways for fluid flow, especially in reservoirs with low matrix permeability, where they constitute the primary flow conduits. Understanding the spatial distribution of natural fracture networks is thus key to optimising production. The impact of fracture systems on fluid flow patterns can be predicted using discrete fracture network models, which allow not only the 6 independent components of the second‐rank permeability tensor to be estimated, but also the 21 independent components of the fully anisotropic fourth‐rank elastic stiffness tensor, from which the elastic and seismic properties of the fractured rock medium can be predicted. As they are stochastically generated, discrete fracture network realisations are inherently non‐unique. It is thus important to constrain their construction, so as to reduce their range of variability and, hence, the uncertainty of fractured rock properties derived from them. This paper presents the underlying theory and implementation of a method for constructing a geologically realistic discrete fracture network, constrained by seismic amplitude variation with offset and azimuth data. Several different formulations are described, depending on the type of seismic data and prior geologic information available, and the relative strengths and weaknesses of each approach are compared. Potential applications of the method are numerous, including the prediction of fluid flow, elastic and seismic properties of fractured reservoirs, model‐based inversion of seismic amplitude variation with offset and azimuth data, and the optimal placement and orientation of infill wells to maximise production.     

A statistical review of mudrock elastic anisotropy

Mudrocks, defined to be fine‐grained siliclastic sedimentary rocks such as siltstones, claystones, mudstones and shales, are often anisotropic due to lamination and microscopic alignments of clay platelets. The resulting elastic anisotropy is often non‐negligible for many applications in the earth sciences such as wellbore stability, well stimulation and seismic imaging. Anisotropic elastic properties reported in the open literature have been compiled and statistically analysed. Correlations between elastic parameters are observed, which will be useful in the typical case that limited information on a rock's elastic properties is known. For example, it is observed that the highest degree of correlation is between the horizontal elastic stiffnesses C₁₁ and C₆₆. The results of statistical analysis are generally consistent with prior observations. In particular, it is observed that Thomsen's ? and γ parameters are almost always positive, Thomsen's ? and γ parameters are well correlated, Thomsen's δ is most frequently small and Thomsen's ? is generally larger than Thomsen's δ. These observations suggest that the typical range for the elastic properties of mudrocks span a sub‐space less than the five elastic constants required to fully define a Vertical Transversel Isotropic medium. Principal component analysis confirms this and that four principal components can be used to span the space of observed elastic parameters.     

Effect of fracture fill on frequency‐dependent anisotropy of fractured porous rocks

In fractured reservoirs, seismic wave velocity and amplitude depend on frequency and incidence angle. Frequency dependence is believed to be principally caused by the wave‐induced flow of pore fluid at the mesoscopic scale. In recent years, two particular phenomena, i.e., patchy saturation and flow between fractures and pores, have been identified as significant mechanisms of wave‐induced flow. However, these two phenomena are studied separately. Recently, a unified model has been proposed for a porous rock with a set of aligned fractures, with pores and fractures filled with two different fluids. Existing models treat waves propagating perpendicular to the fractures. In this paper, we extend the model to all propagation angles by assuming that the flow direction is perpendicular to the layering plane and is independent of the loading direction. We first consider the limiting cases through poroelastic Backus averaging, and then we obtain the five complex and frequency‐dependent stiffness values of the equivalent transversely isotropic medium as a function of the frequency. The numerical results show that, when the bulk modulus of the fracture‐filling fluid is relatively large, the dispersion and attenuation of P‐waves are mainly caused by fractures, and the values decrease as angles increase, almost vanishing when the incidence angle is 90° (propagation parallel to the fracture plane). While the bulk modulus of fluid in fractures is much smaller than that of matrix pores, the attenuation due to the “partial saturation” mechanism makes the fluid flow from pores into fractures, which is almost independent of the incidence angle.     

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.

     

Test of rock physics models for prediction of seismic velocities in shallow unconsolidated sands: a well log data case‡

This paper tests the ability of various rock physics models to predict seismic velocities in shallow unconsolidated sands by comparing the estimates to P and S sonic logs collected in a shallow sand layer and ultrasonic laboratory data of an unconsolidated sand sample. The model fits are also evaluated with respect to the conventional model for unconsolidated sand. Our main approach is to use Hertz‐Mindlin and Walton contact theories, assuming different weight fractions of smooth and rough contact behaviours, to predict the elastic properties of the high porosity point. Using either the Hertz‐Mindlin or Walton theories with rough contact behaviour to define the high porosity endpoint gives an over‐prediction of the velocities. The P‐velocity is overpredicted by a factor of ～1.5 and the S‐velocity by a factor of ～1.8 for highly porous gas‐sand. The degree of misprediction decreases with increasing water saturation and porosity.Using the Hertz‐Mindlin theory with smooth contact behaviour or weighted Walton models gives a better fit to the data, although the data are best described using the Walton smooth model. To predict the properties at the lower porosities, the choice of bounding model attached to the Walton Smooth model controls the degree of fit to the data, where the Reuss bound best captures the porosity variations of dry and wet sands in this case since they are caused by depositional differences. The empirical models based on lab experiments on unconsolidated sand also fit the velocity data measured by sonic logs in situ, which gives improved confidence in using lab‐derived results.     

Water retention effects on elastic properties of Opalinus shale

Shales play an important role in many engineering applications such as nuclear waste, CO₂ storage and oil or gas production. Shales are often utilized as an impermeable seal or an unconventional reservoir. For both situations, shales are often studied using seismic waves. Elastic properties of shales strongly depend on their hydration, which can lead to substantial structural changes. Thus, in order to explore shaly formations with seismic methods, it is necessary to understand the dependency of shale elastic properties on variations in hydration. In this work, we investigate structural changes in Opalinus shale at different hydration states using laboratory measurements and X-ray micro-computed tomography. We show that the shale swells with hydration and shrinks with drying with no visible damage. The pore space of the shale deforms, exhibiting a reduction in the total porosity with drying and an increase in the total porosity with hydration. We study the elastic properties of the shale at different hydration states using ultrasonic velocities measurements. The elastic moduli of the shale show substantial changes with variations in hydration, which cannot be explained with a single driving mechanism. We suggest that changes of the elastic moduli with variations in hydration are driven by multiple competing factors: (1) variations in total porosity, (2) substitution of pore-filling fluid, (3) change in stiffness of contacts between clay particles and (4) chemical hardening/softening of clay particles. We qualitatively and quantitatively analyse and discuss the influence of each of these factors on the elastic moduli. We conclude that depending on the microstructure and composition of a particular shale, some of the factors dominate over the others, resulting in different dependencies of the elastic moduli on hydration.     

A rock physics model to map gross lithology using compaction

Differential compaction has long been used by seismic interpreters to infer subsurface geology using knowledge of the relative compaction of different types of sediments. We outline a method to infer the gross fraction of shale in an interval between two seismic horizons using sandstone and shale compaction laws. A key component of the method involves reconstruction of a smooth depositional horizon by interpolating decompacted thicknesses from well control. We derive analytic formulae for decompaction calculations using known porosity–stress relations and do not employ discrete layer iterative methods; these formulae were found to depend not only upon the gross fraction of shale but also on the clay content of the shales and the thickness of the interval. The relative merits of several interpolation options were explored, and found to depend upon the structural setting. The method was successfully applied to an oil sands project in Alberta, Canada.     

孔隙-裂隙性质和黏土含量对页岩油层系致密岩石弹性波耗散规律的影响研究

作为一种非常规油气资源,页岩油储量丰富、分布范围广,具有巨大的勘探开发潜力,是近年来油气产业关注的重点与热点.然而,页岩油储层具有岩石矿物组分多样、低孔低渗、孔隙结构复杂、非均质性强等特征,与常规油气资源存在明显差异.本研究选取鄂尔多斯盆地中生界延长组长7油层组的10块致密砂岩样本,基于X射线衍射分析得到各样本的矿物组分,开展不同围压和流体条件下的超声波实验观测,进而获得样本的纵、横波速度和纵波衰减逆品质因子.基于实验测量获得变压力条件下的孔隙度,结合线性外推的方法,估算各样本的裂隙孔隙度,代入EIAS（Equivalent Inclusion-Average Stress,等效嵌入体应力平均）模型,求取对应的裂隙纵横比和裂隙密度,分析页岩油储层孔隙-裂隙性质对纵波衰减的影响.结果显示相对于衰减,致密砂岩总孔隙度、裂隙纵横比、裂隙密度和衰减变化量（不同围压下的衰减观测值与最大围压下的衰减观测值的差）之间的相关性更加明显.基于薄片分析,结果显示致密样本存在孔内黏土包体、微裂隙包体和粒间孔的三重孔隙结构,因此本文引入三重孔隙结构模型,定量估算各样本的孔内黏土含量,进而分析孔内黏土含量及总黏土含量和纵波衰减之间的关系.结果显示孔内黏土含量是主导页岩油储层纵波衰减大小的主要因素之一,而非总黏土含量.本研究可为页岩油储层衰减特征分析、岩石物理模型构建及地震勘探方法研究提供理论支撑.

     

Spatial constrained inverse rock physics modelling

Predicting reservoir parameters, such as porosity, lithology, and saturations, from geophysical parameters is a problem with non‐unique solutions. The variance in solutions can be extensive, especially for saturation and lithology. However, the reservoir parameters will typically vary smoothly within certain zones—in vertical and horizontal directions. In this work, we integrate spatial correlations in the predicted parameters to constrain the range of predicted solutions from a particular type of inverse rock physics modelling method. Our analysis is based on well‐log data from the Glitne field, where vertical correlations with depth are expected. It was found that the reservoir parameters with the shortest depth correlation (lithology and saturation) provided the strongest constraint to the set of solutions. In addition, due to the interdependence between the reservoir parameters, constraining the predictions by the spatial correlation of one parameter also reduced the number of predictions of the other two parameters. Moreover, the use of additional constraints such as measured log data at specific depth locations can further narrow the range of solutions.     

Rock physics model for seismic velocity & fluid substitution in sub-resolution interbedded sand–shale sequences

The measured geophysical response of sand – shale sequences is an average over multiple layers when the tool resolution (seismic or well log) is coarser than the scale of sand – shale mixing. Shale can be found within sand – shale sequences as laminations, dispersed in sand pores, as well as load bearing clasts. We present a rock physics framework to model seismic/sonic properties of sub-resolution interbedded shaly sands using the so-called solid and mineral substitution models. This modelling approach stays consistent with the conceptual model of the Thomas–Stieber approach for estimating volumetric properties of shaly sands; thus, this work connects established well log data-based petrophysical workflows with quantitative interpretation of seismic data for modelling hydrocarbon signature in sand – shale sequences. We present applications of the new model to infer thickness of sand – shale lamination (i.e., net to gross) and other volumetric properties using seismic data. Another application of the new approach is fluid substitution in sub-resolution interbedded sand–shale sequences that operate directly at the measurement scale without the need to downscale; such a procedure has many practical advantages over the approach of “first-downscale-and-then-upscale” as it is not very sensitive to errors in estimated sand fraction and end member sand/shale properties and remains stable at small sand/shale fractions.     

不同尺度裂缝对弹性波速度和各向异性影响的实验研究

裂缝广泛分布于地球介质中并且具有多尺度的特点,裂缝尺度对于油气勘探和开发有着重要的意义.本文制作了一组含不同长度裂缝的人工岩样,其中三块含裂缝岩样中的裂缝直径分别为2 mm、3 mm和4 mm,裂缝的厚度都约为0.06 mm,裂缝密度大致相同（分别为4.8%、4.86%和4.86%）.在岩样含水的条件下测试不同方向上的纵横波速度,实验结果表明,虽然三块裂缝岩样中的裂缝密度大致相同,但是含不同直径裂缝岩样的纵横波速度存在差异.在各个方向上,含数量众多的小尺度裂缝的岩样中纵横波速度都明显低于含少量的大尺度裂缝的岩样中纵横波速度.尤其是对纵波速度和SV波速度,在不同尺度裂缝岩样中的差异更明显.在含数量多的小尺度裂缝的岩样中纵波各向异性和横波各向异性最高,而含少量的大尺度的裂缝的岩样中的纵波各向异性和横波各向异性较低.实验测量结果与Hudson理论模型预测结果进行了对比分析,结果发现Hudson理论考虑到了裂缝尺度对纵波速度和纵波各向异性的影响,但是忽略了其对横波速度和横波各向异性的影响.

     

Compaction trend versus seismic anisotropy in shaly formations

Shales comprise more than 60% of sedimentary rocks and form natural seals above hydrocarbon reservoirs. Their sealing capacity is also used for storage of nuclear wastes. The world's most important conventional oil and gas reservoirs have their corresponding source rocks in shale. Furthermore, shale oil and shale gas are the most rapidly expanding trends in unconventional oil and gas. Shales are notorious for their strong elastic anisotropy, i.e., so‐called vertical transverse isotropy. This vertical transverse isotropy, characterised by a vertical axis of invariance, is of practical importance as it is required for correct surface seismic data interpretation, seismic to well tie, and amplitude versus offset analysis. A rather classical paradigm makes a clear link between compaction in shales and the alignment of the clay platelets (main constituent of shales). This would imply increasing anisotropy strength with increasing compaction. Our main purpose is to check this prediction on two large databases in shaly formations (more than 800 samples from depths of 0–6 km) by extracting the major trends in the relation between seismic anisotropy and compaction. The statistical analysis of the database shows that the simultaneous increase in density and velocity, a classical compaction signature, is quite weakly correlated with the anisotropy strength. As a consequence, compaction can be excluded as a major cause of seismic anisotropy, at least in shaly formations. Also, the alignment of the clay platelets can explain most of the anisotropy measurements of both databases. Finally, a method for estimating the orientation distribution function of the clay platelets from the measurement of the anisotropy parameters is suggested.     

Seismic driven probabilistic classification of reservoir facies for static reservoir modelling: a case history in the Barents Sea

In this paper we present a case history of seismic reservoir characterization where we estimate the probability of facies from seismic data and simulate a set of reservoir models honouring seismically‐derived probabilistic information. In appraisal and development phases, seismic data have a key role in reservoir characterization and static reservoir modelling, as in most of the cases seismic data are the only information available far away from the wells. However seismic data do not provide any direct measurements of reservoir properties, which have then to be estimated as a solution of a joint inverse problem. For this reason, we show the application of a complete workflow for static reservoir modelling where seismic data are integrated to derive probability volumes of facies and reservoir properties to condition reservoir geostatistical simulations. The studied case is a clastic reservoir in the Barents Sea, where a complete data set of well logs from five wells and a set of partial‐stacked seismic data are available. The multi‐property workflow is based on seismic inversion, petrophysics and rock physics modelling. In particular, log‐facies are defined on the basis of sedimentological information, petrophysical properties and also their elastic response. The link between petrophysical and elastic attributes is preserved by introducing a rock‐physics model in the inversion methodology. Finally, the uncertainty in the reservoir model is represented by multiple geostatistical realizations. The main result of this workflow is a set of facies realizations and associated rock properties that honour, within a fixed tolerance, seismic and well log data and assess the uncertainty associated with reservoir modelling.     

Relations between static and dynamic moduli of sedimentary rocks

Static moduli of rocks are usually different from the corresponding dynamic moduli. The ratio between them is generally complex and depends on several conditions, including stress state and stress history. Different drainage conditions, dispersion (often associated with pore fluid effects), heterogeneities and strain amplitude, are all potential reasons for this discrepancy. Moreover, comparison of static and dynamic moduli is often hampered and maybe mistaken due to insufficient characterization of anisotropy. This paper gives a review of the various mechanisms causing differences between static and dynamic moduli. By careful arrangements of test conditions, it is possible to isolate the mechanisms so that they can be studied separately. Non-elastic deformation induced by the large static strain amplitudes is particularly challenging, however a linear relationship between non-elastic compliance and stress makes it possible to eliminate also this effect by extrapolation to zero strain amplitude. To a large extent, each mechanism can be expressed mathematically with reasonable precision, thus quantitative relations between the moduli can be established. This provides useful tools for analyses and prediction of rock behaviour. For instance, such relations may be used to predict static stiffness and even strength based on dynamic measurements. This is particularly useful in field situations where only dynamic data are available. Further, by utilizing the possibility for extrapolation of static measurements to zero strain amplitude, dispersion in the range from seismic to ultrasonic frequencies may be studied by a combination of static and dynamic measurements.     

Effect of oil composition on fluid substitution in heavy oil reservoirs

Unlike light oils, heavy oils do not have a well‐established scheme for modelling elastic moduli from dynamic reservoir properties. One of the main challenges in the fluid substitution of heavy oils is their viscoelastic nature, which is controlled by temperature, pressure, and fluid composition. Here, we develop a framework for fluid substitution modelling that is reliable yet practical for a wide range of cold and thermal recovery scenarios in producing heavy oils and that takes into account the reservoir fluid composition, grounded on the effective‐medium theories for estimating elastic moduli of an oil–rock system. We investigate the effect of fluid composition variations on oil–rock elastic moduli with temperature changes. The fluid compositional behaviour is determined by flash calculations. Elastic moduli are then determined using the double‐porosity coherent potential approximation method and the calculated viscosity based on the fluid composition. An increase in temperature imposes two opposing mechanisms on the viscosity behaviour of a heavy‐oil sample: gas liberation, which tends to increase the viscosity, and melting, which decreases the viscosity. We demonstrate that melting dominates gas liberation, and as a result, the viscosity and, consequently, the shear modulus of the heavy oils always decrease with increasing temperature. Furthermore, it turns out that one can disregard the effects of gas in the solution when modelling the elastic moduli of heavy oils. Here, we compare oil–rock elastic moduli when the rock is saturated with fluids that have different viscosity levels. The objective is to characterize a unique relation between the temperature, the frequency, and the elastic moduli of an oil–rock system. We have proposed an approach that takes advantage of this relation to find the temperature and, consequently, the viscosity in different regions of the reservoir.     

基于页岩岩石物理等效模型的地应力预测方法研究

地应力的精确预测是对页岩地层进行水平井钻井轨迹设计和压裂的基础.本文在分析页岩构造特征的基础上, 提出了适用于页岩地层的岩石物理等效模型的建立流程, 并以此为基础实现了最小水平地应力的有效预测.首先, 通过分析页岩地层的矿物、孔隙、流体及各向异性特征, 将其等效为具有垂直对称轴的横向各向同性介质, 进行了页岩岩石物理等效模型的构建;然后建立了页岩地层纵横波速度经验公式, 并将该经验公式与岩石物理等效模型均应用于实际页岩工区的横波速度预测中, 二者对比表明, 本文中建立的页岩气岩石物理等效模型具有更高的横波预测精度, 验证了该模型的适用性;最后, 利用该模型计算各弹性刚度张量, 进而实现了页岩地层最小水平地应力的预测, 与各向同性模型估测结果对比表明, 该模型预测的最小水平地应力与地层瞬间闭合压力一致性更高, 且储层位置更为明显, 具有较高的实用性.     

Rock physics modelling based on depositional and burial history of Barents Sea sandstones

Understanding how physical properties and seismic signatures of present day rocks are related to ancient geological processes is important for enhanced reservoir characterization. In this paper, we have studied this relationship for the Kobbe Formation sandstone in the Barents Sea. These rocks show anomalous low shear velocities and high V_P/V_S ratios, which does not agree well with conventional rock physics models for moderately to well consolidated sandstones. These sandstones have been buried relatively deeply and subsequently uplifted 1–2 km. We compared well log data of the Kobbe sandstone with velocity–depth trends modelled by integrating basin modelling principles and rock physics. We found that more accurate velocity predictions were obtained when first honouring mechanical and chemical compaction during burial, followed by generation of micro-cracks during uplift. We suspect that these micro-cracks are formed as overburden is eroded, leading to changes in the subsurface stress-field. Moreover, the Kobbe Formation is typically heterogeneous and characterized by structural clays and mica that can reduce the rigidity of grain contacts. By accounting for depositional and burial history, our velocity predictions become more consistent with geophysical observables. Our approach yields more robust velocity predictions, which are important in prospect risking and net erosion estimates.     

基于微纳米孔隙理论的页岩气储层岩石物理建模方法

页岩储层由于其复杂的构造和孔隙特征,目前一般的岩石物理模型无法对其进行精确描述.微纳米孔隙作为页岩气主要的储集空间,对页岩整体弹性参数有较大影响.干酪根作为页岩中重要的有机质矿物,在页岩中的赋存状态随成熟度不同而变化,同时干酪根也是纳米级孔隙的主要发育场所.目前常规的岩石物理建模方法没有体现微纳米孔隙的作用,同时较少考虑不同成熟度下干酪根对页岩储层弹性性质的影响.本文采用一种微纳米孔隙理论描述页岩微纳米孔隙特性,考虑微纳米孔隙和不同成熟度下干酪根的赋存状态,应用上述微纳米孔隙模型、各向异性SCA-DEM模型、各向异性Eshelby-Cheng模型和Brown-Korringa固体替换方程等建立一种新的页岩储层岩石物理模型.利用中国西南某工区页岩气井对该模型进行验证,模型预测的横波速度与测井速度拟合较好.结果表明不同干酪根成熟度的页岩岩石物理建模结果具有一定的差异,据此可大致区分该工区井的干酪根成熟度;最后对微纳米孔参数进行正演分析,结果反映了页岩的纵横波速度随微纳米孔隙参数的变化趋势.

     

Rock physics modelling and inversion for saturation-pressure changes in time-lapse seismic studies

Time-lapse seismic data are generally used to monitor the changes in dynamic reservoir properties such as fluid saturation and pore or effective pressure. Changes in saturation and pressure due to hydrocarbon production usually cause changes in the seismic velocities and as a consequence changes in seismic amplitudes and travel times. This work proposes a new rock physics model to describe the relation between saturation-pressure changes and seismic changes and a probabilistic workflow to quantify the changes in saturation and pressure from time-lapse seismic changes. In the first part of this work, we propose a new quadratic approximation of the rock physics model. The novelty of the proposed formulation is that the coefficients of the model parameters (i.e. the saturation-pressure changes) are functions of the porosity, initial saturation and initial pressure. The improvements in the results of the forward model are shown through some illustrative examples. In the second part of the work, we present a Bayesian inversion approach for saturation-pressure 4D inversion in which we adopt the new formulation of the rock physics approximation. The inversion results are validated using synthetic pseudo-logs and a 3D reservoir model for CO₂ sequestration.