Testing Gassmann fluid substitution: sonic logs versus ultrasonic core measurements

Although Gassmann fluid substitution is standard practice for time-lapse studies, its validity in the field environment rests upon a number of underlying assumptions. The impact of violation on the predictions of Gassmann equations can only ultimately be validated by in situ testing in real geological environments. In this paper we show a workflow that we developed to test Gassmann fluid substitution by comparing saturated P-wave moduli computed from dry core measurements against those obtained from sonic and density logs. The workflow has been tested on 43 samples taken from a 45 m turbidite reservoir from the Campos Basin, offshore Brazil. The results show good statistical agreement between the P-wave elastic moduli computed from cores using the Gassmann equation with the corresponding moduli computed from log data. This confirms that all the assumptions of the Gassmann are adequate within the measurement error and natural variability of elastic properties. These results provide further justification for using the Gassmann theory to interpret time-lapse effects in this sandstone reservoir and in similar geological formations.     

饱和碳酸盐岩地震频带弹性参数响应的实验机理分析研究: 压力与孔隙流体影响

碳酸盐岩储层中蕴藏着全球近一半油气储量,也是我国深层、超深层的重点勘探领域.然而,深层碳酸盐岩复杂孔隙结构导致其储层条件下岩石物理响应机理不明,这对有效地震储层表征与流体预测带来了巨大挑战.目前,国内尚缺乏系统开展针对深层碳酸盐岩储层的地震频带岩石物理实验测试研究.厘清深层油藏开发中因流体流动而引起的储层压力场与孔隙流体性质变化对地震频带弹性参数影响机制,在一系列地球物理应用中具有十分重要的意义.通过开展跨频带（地震低频+超声高频）弹性参数实验测试,本文系统研究了压力与孔隙流体对深层碳酸盐岩弹性模量及其衰减的影响机制.针对中低孔渗碳酸盐岩储层岩芯,分别测量了其在干燥、饱和盐水与甘油下的弹性参数,分析了弹性模量对压力与频率敏感性.干燥岩芯杨氏模量频变特性显著低于饱和流体岩芯实测数据,且饱和甘油岩芯模量及其衰减均高于饱和盐水测量结果.部分饱和盐水岩芯的地震频带实测结果表明,杨氏模量与泊松比均随含水饱和度升高而增大,其频散程度却略有降低.此外,基于干燥岩芯弹性参数不依赖频率的前提,受迫振动法低频实验所得岩石弹性模量和衰减数据与三孔隙类型喷射流模型预测结果相一致,证实喷射流是引起复杂孔隙微观结构储层岩芯频变黏弹性响应的主控因素.

     

The added value of joint PP–PS inversion for reservoir characterization: A case study using Jubarte PRM seismic data (offshore Brazil)

The added value of the joint pre-stack inversion of PP (incident P-wave and reflected P-wave) and PS (incident P-wave and reflected S-wave) seismic data for the time-lapse application is shown. We focus on the application of this technique to the time-lapse (four-dimensional) multicomponent Jubarte field permanent reservoir monitoring seismic data. The joint inversion results are less sensitive to noise in the input data and show a better match with the rock physics models calibrated for the field. Further, joint inversion improves S-impedance estimates and provides a more robust quantitative interpretation, allowing enhanced differentiation between pore pressure and fluid saturation changes, which will be extremely useful for reservoir management. Small changes in reservoir properties are expected in the short time between the time-lapse seismic acquisitions used in the Jubarte project (only 1 year apart). The attempt to recover subtle fourth-dimensional effects via elastic inversion is recurrent in reservoir characterization projects, either due to the small sensitivity of the reservoirs to fluid and pressure changes or the short interval between the acquisitions. Therefore, looking for methodologies that minimize the uncertainty of fourth-dimensional inversion outputs is of fundamental importance. Here, we also show the differences between PP only and joint PP–PS inversion workflows and parameterizations that can be applied in other projects. We show the impact of using multicomponent data as input for elastic seismic inversions in the analysis of the time-lapse differences of the elastic properties. The larger investment in the acquisition and processing of multicomponent seismic data is shown to be justified by the improved results from the fourth-dimensional joint inversion.     

陆相薄互层稠油油藏热采时移地震监测研究

目前,针对陆相薄互层油藏实施时移地震监测尚没有明显的突破,加强时移地震方法、理论的研究和应用,对于我国时移地震监测技术的发展和应用具有积极的意义.根据油藏工程理论,在详细分析火烧油层对储层物性影响的基础上,结合已有的实验室岩石物理测量结果,重点就稠油热采过程中温度的剧烈变化对储层岩石和孔隙流体弹性特性的影响进行了较为详细的分析.并开展了薄互层油藏火烧油层地震正演模拟研究.结果表明,在稠油热采过程中,高温高压不仅会使得孔隙流体特性发生显著的改变,而且储层岩石本身弹性特性的变化也非常明显.即使是对于薄层或薄互层,两方面共同的变化将使得稠油热采前后储层弹性特性产生巨大的差异,进而引起显著的地震异常.因此,开展陆相薄互层稠油热采时移地震监测,不仅具有坚实的岩石物理基础,而且具有切实的可行性.     

Iterated extended Kalman filter method for time-lapse seismic full-waveform inversion

Time-lapse seismic data is useful for identifying fluid movement and pressure and saturation changes in a petroleum reservoir and for monitoring of CO₂ injection. The focus of this paper is estimation of time-lapse changes with uncertainty quantification using full-waveform inversion. The purpose of also estimating the uncertainty in the inverted parameters is to be able to use the inverted seismic data quantitatively for updating reservoir models with ensemble-based methods. We perform Bayesian inversion of seismic waveform data in the frequency domain by combining an iterated extended Kalman filter with an explicit representation of the sensitivity matrix in terms of Green functions (acoustic approximation). Using this method, we test different strategies for inversion of the time-lapse seismic data with uncertainty. We compare the results from a sequential strategy (making a prior from the monitor survey using the inverted baseline survey) with a double difference strategy (inverting the difference between the monitor and baseline data). We apply the methods to a subset of the Marmousi2 P-velocity model. Both strategies performed well and relatively good estimates of the monitor velocities and the time-lapse differences were obtained. For the estimated time-lapse differences, the double difference strategy gave the lowest errors.     

地震尺度下碳酸盐岩储层的岩石物理建模方法(英文)

碳酸盐岩油藏的强非均质性以及孔隙结构的复杂性,使得作为连接油藏参数与地震参数重要桥梁的岩石物理模型,以及作为油藏预测和定量表征最有效工具的流体替换成为岩石物理建模的难点与重点。在碳酸盐岩储层复杂孔隙结构与地震尺度下碳酸盐岩储层非均质性分析基础上,研究采用岩石网格化方法,将地震尺度下非均质碳酸盐岩储层岩石划分为具有独立岩石参数的均质岩石子体,根据岩石孔隙成因与结构特征采用不同岩石物理模型分步计算岩石子块干岩石弹性模量,并根据不同孔隙连通性进行流体替换,计算饱和不同流体岩石弹性模量。基于计算的岩石子块弹性模量,采用Hashin-Shtrikman-Walpole弹性边界计算理论方法实现地震尺度下碳酸盐岩储层弹性参数计算。通过对含有不同类型孔隙组合碳酸盐岩储层模型的弹性模量进行计算与分析,明确不同孔隙对岩石弹性参数的影响特征,模拟分析结果与实际资料认识一致。     

油藏水驱开采时移地震监测岩石物理基础测量

岩石物理测量是油藏水驱开采时移地震监测的基础.在实验室对来自胜利油田的5块岩石样品模拟储层条件进行了水驱和气驱动态岩石物理弹性测量,重点分析了流体替换、温度、孔隙压力对岩石纵、横波速度的影响.实验表明,在水驱情形下,由于流体替换和温度、孔隙压力变化所引起的岩石纵横波速度的变化均很小,实施时移地震监测具有较大的风险性.相比之下,气驱可能引起较为明显的纵波速度变化,有利于时移地震监测的实施.进一步完善实验方法、丰富实验内容、是今后时移地震岩石物理实验研究的主要任务.     

Anisotropic 4D seismic response inferred from ultrasonic laboratory measurements: A direct comparison with the isotropic response

Pore-pressure depletion causes changes in the triaxial stress state. Pore-pressure depletion in a flat reservoir, for example, can be reasonably approximated as uniaxial compaction, in which the horizontal effective stress change is smaller than the vertical effective stress. Furthermore, the stress sensitivity of velocities can be angle-dependent. Therefore, time-lapse changes in reservoir elastic anisotropy are expected as a consequence of production, which can complicate the interpretation of the 4D seismic response. The anisotropic 4D seismic response caused by pore-pressure depletion was investigated using existing core velocity measurements. To make a direct comparison between the anisotropic 4D seismic response and the isotropic response based only on vertical velocities, pseudoisotropic elastic properties were utilized, and the two responses were compared in terms of a dynamic rock physics template. A comparison of the dynamic rock physics templates indicates that time-lapse changes in reservoir elastic anisotropy have a noticeable impact on the interpretation of 4D seismic data. Changes in anisotropy as a result of pore-pressure depletion cause a time-lapse amplitude variation with offset response as if there is a reduction in V_P/V_S (i.e., pseudoisotropic V_P/V_S decreases), although the vertical V_P/V_S increases. The impact of time-lapse changes in anisotropy on the amplitude variation with offset gradient was also investigated, and the time-lapse anisotropy was found to enhance changes in the amplitude variation with offset gradient for a given case.     

Modelling elastic properties of impure chalk from South Arne Field, North Sea

In impure chalk, the elastic moduli are not only controlled by porosity but also by contact‐cementation, resulting in relatively large moduli for a given porosity, and by admixtures of clay and fine silica, which results in relatively small moduli for a given porosity. Based on a concept of solids suspended in pore fluids as well as composing the rock frame, we model P‐wave and S‐wave moduli of dry and wet plug samples by an effective‐medium Hashin–Shtrikman model, using chemical, mineralogical and textural input. For a given porosity, the elastic moduli correspond to a part of the solid (the iso‐frame value) forming the frame of an Upper Hashin–Shtrikman bound, whereas the remaining solid is modelled as suspended in the pore fluid. The iso‐frame model is thus a measure of the pore‐stiffness or degree of cementation of the chalk. The textural and mineralogical data may be assessed from logging data on spectral gamma radiation, density, sonic velocity and water saturation in a hydrocarbon zone, whereas the iso‐frame value of a chalk may be assessed from the density and acoustic P‐wave logs alone. The iso‐frame concept may thus be directly used in conventional log‐analysis and is a way of incorporating sonic‐logging data. The Rigs‐1 and Rigs‐2 wells in the South Arne field penetrate the chalk at the same depth but differ in porosity and in water saturation although almost the entire chalk interval has irreducible water saturation. Our model, combined with petrographic data, indicates that the difference in porosity is caused by a higher degree of pore‐filling cementation in Rigs‐1. Petrographic data indicate that the difference in water saturation is caused by a higher content of smectite in the pores of Rigs‐1. In both wells, we find submicron‐size diagenetic quartz.     

Asymmetry in the time-lapse seismic response to injection and depletion

Large changes in seismic reflection amplitude have been observed around injectors, and result from the decrease in elastic‐wave velocity due to the increase in pore pressure in the reservoir. In contrast, the velocity change resulting from the decrease in pore pressure in depleting reservoirs is observed to be smaller in magnitude. Elastic‐wave velocities in sandstones vary with stress due to the presence of stress‐sensitive grain boundaries within the rock. Grain‐boundary stiffness increases non‐linearly with increasing compressive stress, due to increased contact between opposing faces of the boundary. This results in a change in velocity due to a decrease in pore pressure that is smaller than the change in velocity caused by an increase in pore pressure, in agreement with time‐lapse seismic observations. The decrease in porosity resulting from depletion is not fully recovered upon re‐pressurization, and this leads to an additional steepening of the velocity vs. effective stress curve for injection relative to depletion. This difference is enhanced by any breakage of cement or weakening of grain contacts that may occur during depletion and by the reopening or formation of fractures or joints and dilation of grain boundaries that may occur during injection.     

模拟天然气水合物的岩石物理特性模型实验

针对水合物沉积的悬浮、颗粒接触和胶结三种微观模式,制作一组微弱胶结非固结高孔隙度人造样品和颗粒填充渐变的三维物理模型. 通过物理模型实验研究天然气水合物物性参数的敏感性. 实验结果表明：在弱颗粒间胶结物和低有效应力的固结差的沉积物中,声波对孔隙流体性质较敏感. 随着温度的降低颗粒胶结,改变原有沉积物的岩石物理特性,速度、弹性模量和频率升高,声波衰减和Vp/VS减小,沉积层内的反射波消隐.     

An Estimation Method of Pore Structure and Mineral Moduli Based on Kuster-Toksöz (KT) Model and Biot’s Coefficient

Pore structure and mineral matrix elastic moduli are indispensable in rock physics models. We propose an estimation method of pore structure and mineral moduli based on Kuster-Toksöz model and Biot’s coefficient. In this technique, pore aspect ratios of five different scales from 100 to 10^?4 are considered, Biot’s coefficient is used to determine bounds of mineral moduli, and an estimation procedure combined with simulated annealing (SA) algorithm to handle real logs or laboratory measurements is developed. The proposed method is applied to parameter estimations on 28 sandstone samples, the properties of which have been measured in lab. The water saturated data are used for estimating pore structure and mineral moduli, and the oil saturated data are used for testing these estimated parameters through fluid substitution in Kuster-Toksöz model. We then compare fluid substitution results with lab measurements and find that relative errors of P-wave and S-wave velocities are all less than 5%, which indicates that the estimation results are accurate.     

POROSITY AND PORE STRUCTURE FROM ACOUSTIC WELL LOGGING DATA1

Wyllie's time-average equation and subsequent refinements have been used for over 20 years to estimate the porosity of reservoir rocks from compressional (P)-wave velocity (or its reciprocal, transit time) recorded on a sonic log. This model, while simple, needs to be more convincingly explained in theory and improved in practice, particularly by making use of shear (S)-wave velocity. One of the most important, although often ignored, factors affecting elastic velocities in a rock is pore structure, which is also a controlling factor for transport properties of a rock. Now that S-wave information can be obtained from the sonic log, it may be used with P-waves to provide a better understanding of pore structure. A new acoustic velocities-to-porosity transform based on an elastic velocity model developed by Kuster and Toksöz is proposed. Employing an approximation to an equivalent pore aspect ratio spectrum, pore structure for reservoir rocks is taken into account, in addition to total pore volume. Equidimensional pores are approximated by spheres and rounded spheroids, while grain boundary pores and flat pores are approximated by low aspect ratio cracks. An equivalent pore aspect ratio spectrum is characterized by a power function which is determined by compressional-and shear-wave velocities, as well as by matrix and inclusion properties. As a result of this more sophisticated elastic model of porous rocks and a stricter theory of elastic wave propagation, the new method leads to a more satisfactory interpretation and fuller use of seismic and sonic log data. Calculations using the new transform on data for sedimentary rocks, obtained from published literature and laboratory measurements, are presented and compared at atmospheric pressure with those estimated from the time-average equation. Results demonstrate that, to compensate for additional complexity, the new method provides more detailed information on pore volume and pore structure of reservoir rocks. Examples are presented using a realistic self-consistent averaging scheme to consider interactions between pores, and the possibility of extending the method to complex lithologies and shaly rocks is discussed.     

时移地震资料贝叶斯AVO波形反演

针对时移地震差异数据,给出了一种基于贝叶斯理论的AVO波形反演方法.该方法可以利用时移地震差异数据同时反演出纵波阻抗、横波阻抗和密度的变化.利用时移地震资料进行反演,由于采集和处理过程中存在一定的差异,不同年份地震资料在非注采过程影响区域也会存在一定的变化,而该变化会导致反演结果在非注采区域有较大的变化.针对这一问题,本文采用贝叶斯理论框架,将待求的纵横波阻抗、密度变化的先验信息和包含在地震数据中的信息结合起来,对于纵横波阻抗和密度变化,假设其服从Gauss分布,并以时移地震分别反演的结果作为其期望,同时,为了更好地表征储层属性变化,提高分辨率和抑制非注采区域弹性参数的变化,假设弹性参数变化的导数服从改进的Cauchy分布.数值模拟试验和实际资料处理结果皆表明,本文提出的反演方法能够有效地抑制假象,突出储层性质的变化,得到高分辨率的弹性参数变化信息,为研究储层属性的变化和优化开采方案提供更多的有效的信息.     

时移地震资料贝叶斯AVO波形反演

针对时移地震差异数据,给出了一种基于贝叶斯理论的AVO波形反演方法.该方法可以利用时移地震差异数据同时反演出纵波阻抗、横波阻抗和密度的变化.利用时移地震资料进行反演,由于采集和处理过程中存在一定的差异,不同年份地震资料在非注采过程影响区域也会存在一定的变化,而该变化会导致反演结果在非注采区域有较大的变化.针对这一问题,本文采用贝叶斯理论框架,将待求的纵横波阻抗、密度变化的先验信息和包含在地震数据中的信息结合起来,对于纵横波阻抗和密度变化,假设其服从Gauss分布,并以时移地震分别反演的结果作为其期望,同时,为了更好地表征储层属性变化,提高分辨率和抑制非注采区域弹性参数的变化,假设弹性参数变化的导数服从改进的Cauchy分布.数值模拟试验和实际资料处理结果皆表明,本文提出的反演方法能够有效地抑制假象,突出储层性质的变化,得到高分辨率的弹性参数变化信息,为研究储层属性的变化和优化开采方案提供更多的有效的信息.     

Integrating basin modeling with seismic technology and rock physics

We explore the link between basin modelling and seismic inversion by applying different rock physics models. This study uses the E‐Dragon II data in the Gulf of Mexico. To investigate the impact of different rock physics models on the link between basin modelling and seismic inversion, we first model relationships between seismic velocities and both (1) porosity and (2) effective stress for well‐log data using published rock physics models. Then, we build 1D basin models to predict seismic velocities derived from basin modelling with different rock physics models, in a comparison with average sonic velocities measured in the wells. Finally, we examine how basin modelling outputs can be used to aid seismic inversion by providing constraints for the background low‐frequency model. For this, we run different scenarios of inverting near angle partial stack seismic data into elastic impedances to test the impact of the background model on the quality of the inversion results. The results of the study suggest that the link between basin modelling and seismic technology is a two‐way interaction in terms of potential applications, and the key to refine it is establishing a rock physics models that properly describes changes in seismic signatures reflecting changes in rock properties.     

超深层碳酸盐岩储层地震岩石物理特征和模型表征

揭示超深层碳酸盐岩储层的地震岩石物理响应机理可以为深储层测井数据解释、地球物理预测提供物理基础, 对于深层油气勘探开发、向地球深部进军都有重要意义.深层致密碳酸盐岩储层面临着高温高压、成岩作用显著、异常压力普遍等新的物理环境, 其岩石骨架、储集非均质、以及流体属性都将发生系统的变化.通过对塔里木盆地超深层(＞7000m)样品的弹性性质测量, 系统的研究了深层碳酸盐岩储层的压力效应和水饱和流体效应, 厘清了控制深层碳酸盐岩储层地震弹性性质的二元主控因素: 裂隙发育和流体类型.且这二者呈现明显的耦合关系, 裂隙越发育, 越有利于识别不同流体的弹性特征.深层碳酸盐岩样品整体显示弱VTI(垂直横向各向同性)各向异性特征(＜4%), 也反映了在微观尺度上, 水平裂隙相较于垂直裂隙对地震各向异性的影响更大.孔隙压力和气油比(GOR)对深层条件下油气流体的弹性响应也有较大影响: 油气流体的弹性模量随着气油比的增加呈现明显下降, 但随着孔隙压力的增加呈现升高趋势.在深储层地震岩石物理响应机理的基础上, 建立了表征深层碳酸盐岩储层二元主控因素的地震岩石物理模型, 该模型可以有效的刻画裂隙密度、流体类型对深层碳酸盐岩储层地震弹性特征的影响, 但用于实际饱和度的定量解释仍存在一定不确定性.

     

Modeling and interpretation of Q logs in carbonate rock using a double porosity model and well logs

Attenuation data extracted from full waveform sonic logs is sensitive to vuggy and matrix porosities in a carbonate aquifer. This is consistent with the synthetic attenuation (1 / Q) as a function of depth at the borehole-sonic source-peak frequency of 10 kHz. We use velocity and densities versus porosity relationships based on core and well log data to determine the matrix, secondary, and effective bulk moduli. The attenuation model requires the bulk modulus of the primary and secondary porosities. We use a double porosity model that allows us to investigate attenuation at the mesoscopic scale. Thus, the secondary and primary porosities in the aquifer should respond with different changes in fluid pressure. The results show a high permeability region with a Q that varies from 25 to 50 and correlates with the stiffer part of the carbonate formation. This pore structure permits water to flow between the interconnected vugs and the matrix. In this region the double porosity model predicts a decrease in the attenuation at lower frequencies that is associated with fluid flowing from the more compliant high-pressure regions (interconnected vug space) to the relatively stiff, low-pressure regions (matrix). The chalky limestone with a low Q of 17 is formed by a muddy porous matrix with soft pores. This low permeability region correlates with the low matrix bulk modulus. A low Q of 18 characterizes the soft sandy carbonate rock above the vuggy carbonate.This paper demonstrates the use of attenuation logs for discriminating between lithology and provides information on the pore structure when integrated with cores and other well logs. In addition, the paper demonstrates the practical application of a new double porosity model to interpret the attenuation at sonic frequencies by achieving a good match between measured and modeled attenuation.     

A triple porosity scheme for fluid/solid substitution: theory and experiment

Quantifying the effects of pore-filling materials on elastic properties of porous rocks is of considerable interest in geophysical practice. For rocks saturated with fluids, the Gassmann equation is proved effective in estimating the exact change in seismic velocity or rock moduli upon the changes in properties of pore infill. For solid substance or viscoelastic materials, however, the Gassmann theory is not applicable as the rigidity of the pore fill (either elastic or viscoelastic) prevents pressure communication in the pore space, which is a key assumption of the Gassmann equation. In this paper, we explored the elastic properties of a sandstone sample saturated with fluid and solid substance under different confining pressures. This sandstone sample is saturated with octadecane, which is a hydrocarbon with a melting point of 28°C, making it convenient to use in the lab in both solid and fluid forms. Ultrasonically measured velocities of the dry rock exhibit strong pressure dependency, which is largely reduced for the filling of solid octadecane. Predictions by the Gassmann theory for the elastic moduli of the sandstone saturated with liquid octadecane are consistent with ultrasonic measurements, but underestimate the elastic moduli of the sandstone saturated with solid octadecane. Our analysis shows that the difference between the elastic moduli of the dry and solid-octadecane-saturated sandstone is controlled by the squirt flow between stiff, compliant, and the so-called intermediate pores (with an aspect ratio larger than that of compliant pore but much less than that of stiff pores). Therefore, we developed a triple porosity model to quantify the combined squirt flow effects of compliant and intermediate pores saturated with solid or viscoelastic infill. Full saturation of remaining stiff pores with solid or viscoelastic materials is then considered by the lower embedded bound theory. The proposed model gave a reasonable fit to the ultrasonic measurements of the elastic moduli of the sandstone saturated with liquid or solid octadecane. Comparison of the predictions by the new model to other solid substitution schemes implied that accounting for the combined effects of compliant and intermediate pores is necessary to explain the solid squirt effects.     

Quantitative pore-type characterization from well logs based on the seismic petrophysics in a carbonate reservoir

Quality, availability and consistency of the measured and interpreted well log data are essential in the seismic reservoir characterization methods, and seismic petrophysics is the recommended workflow to achieve data consistency between logs and seismic domains. This paper uses seismic petrophysics workflow to improve well logs and pore geometry interpretations for an oil carbonate reservoir in the Fahliyan Formation in the southwest of Iran. The petrophysical interpreted well logs, rock physics and well-to-seismic tie analysis are integrated into the proposed workflow. Our implementation incorporates revising petrophysical well log interpretations and updating pore geometry characteristics to obtain a better well-tie quality. We first propose an improved pore-type characterization approach based on both P- and S-wave velocities for quantifying pore geometry. Then, seismic logs are estimated accordingly, and the results are used in the well-to-seismic analysis. The quality of the well-tie is improved, furthermore, by iterating on the petrophysical interpreted well logs as well as the calculated pore geometries. For the intervals with high-quality data, our workflow improves the consistency between the results of measured and modelled seismic logs. For the intervals with problematic well logs, the application of our proposed workflow results in the successful replacement of the poor data and subsequently leads to an improved wavelet estimation and well-tie results. In both cases, a higher quantification of pore geometries is achieved, which in turn is confirmed by the core images and formation micro-imager analysis.