Sensitivity of time-lapse seismic to reservoir stress path

The change in reservoir pore pressure due to the production of hydrocarbons leads to anisotropic changes in the stress field acting on the reservoir. Reservoir stress path is defined as the ratio of the change in effective horizontal stress to the change in effective vertical stress from the initial reservoir conditions, and strongly influences the depletion‐induced compaction behaviour of the reservoir. Seismic velocities in sandstones vary with stress due to the presence of stress‐sensitive regions within the rock, such as grain boundaries, microcracks, fractures, etc. Since the response of any microcracks and grain boundaries to a change in stress depends on their orientation relative to the principal stress axes, elastic‐wave velocities are sensitive to reservoir stress path. The vertical P‐ and S‐wave velocities, the small‐offset P‐ and SV‐wave normal‐moveout (NMO) velocities, and the P‐wave amplitude‐versus‐offset (AVO) are sensitive to different combinations of vertical and horizontal stress. The relationships between these quantities and the change in stress can be calibrated using a repeat seismic, sonic log, checkshot or vertical seismic profile (VSP) at the location of a well at which the change in reservoir pressure has been measured. Alternatively, the variation of velocity with azimuth and distance from the borehole, obtained by dipole radial profiling, can be used. Having calibrated these relationships, the theory allows the reservoir stress path to be monitored using time‐lapse seismic by combining changes in the vertical P‐wave impedance, changes in the P‐wave NMO and AVO behaviour, and changes in the S‐wave impedance.     

Influence of pore pressure on velocity in low-porosity sandstone: Implications for time-lapse feasibility and pore-pressure study

As seismic data quality improves, time‐lapse seismic data is increasingly being called upon to interpret and predict changes during reservoir development and production. Since pressure change is a major component of reservoir change during production, a thorough understanding of the influence of pore pressure on seismic velocity is critical. Laboratory measurements show that differential pressure (overburden minus fluid pressure) does not adequately determine the actual reservoir conditions. Changes in fluid pressure are found to have an additional effect on the physical properties of rocks. The effective‐stress coefficient n is used to quantify the effect of pore pressure compared to confining pressure on rock properties. However, the current practice in time‐lapse feasibility studies, reservoir‐pressure inversion and pore‐pressure prediction is to assume that n= 1. Laboratory measurements, reported in both this and previous research show that n can be significantly less than unity for low‐porosity rocks and that it varies with porosity, rock texture and wave type. We report the results of ultrasonic experiments to estimate n for low‐porosity sandstones with and without microcracks. Our results show that, for P‐waves, n is as low as 0.4 at a differential pressure of 20 MPa (about 3000 psi) for a low‐porosity sandstone. Thus, in pore‐pressure inversion, an assumption of n= 1 would lead to a 150% underestimation of the pore pressure. Comparison of the effective‐stress coefficient for fractured and unfractured samples suggests that the presence of microfractures increases the sensitivity of P‐wave velocity to pore pressure, and therefore the effective‐stress coefficient. Our results show that the effective‐stress coefficient decreases with the differential pressure, with a higher differential pressure resulting in a lower effective‐stress coefficient. While the effective‐stress coefficient for P‐wave velocity can be significantly less than unity, it is close to one for S‐waves.     

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.     

介观尺度孔隙流体流动作用对纵波传播特征的影响研究——以周期性层状孔隙介质为例

介观尺度孔隙流体流动是地震频段岩石表现出较强速度频散与衰减的主要作用.利用周期性层状孔隙介质模型,基于准静态孔弹性理论给出了模型中孔隙压力、孔隙流体相对运动速度以及固体骨架位移等物理量的数学解析表达式,同时利用Biot理论将其扩展至全频段条件下,克服了传统White模型中介质分界面处流体压力不连续的假设. 在此基础上对准静态与全频段下模型介质中孔隙压力、孔隙流体相对运动速度变化形式及其对弹性波传播特征的影响进行了讨论,为更有效理解介观尺度下流体流动耗散和频散机制提供物理依据.研究结果表明,低频条件下快纵波孔压在介质层内近于定值,慢纵波通过流体扩散改变总孔隙压力, 随频率的增加慢波所形成的流体扩散作用逐渐减弱致使介质中总孔压逐渐接近于快纵波孔压,在较高频率下孔压与应力的二次耦合作用使总孔压超过快纵波孔压.介质中孔隙流体相对运动速度与慢纵波形成的流体相对运动速度变化形式一致;随频率的增加孔隙流体逐渐从排水的弛豫状态过渡到非弛豫状态,其纵波速度-含水饱和度变化形式也从符合孔隙流体均匀分布模式过渡到斑块分布模式,同时介质在不同含水饱和度下的衰减峰值与慢纵波所形成的孔隙流体相对流动速度具有明显的相关性.     

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.     

Deriving effects of pressure depletion on elastic framework moduli from sonic logs

We have developed a method to determine the effect of pore pressure depletion on elastic framework moduli, by utilizing sonic logs from wells drilled at different locations through a reservoir at varying depletion stages. This is done by first inverting the sonic logs for elastic framework bulk and shear moduli, thus carefully removing pressure dependent fluid effects. By crossplotting these elastic framework moduli against an increase in net stress (which is directly related to depletion), we derive the stress sensitivity of the elastic framework moduli. We found that the observed stress sensitivity was consistent with time-lapse seismic results and that the sensitivity derived from the sonic logs was much smaller than predicted by hydrostatic measurements on core samples. This method is applicable to depletion scenarios in mature fields and can be used both for modelling and inverting time-lapse seismic data for effects of pore pressure depletion on seismic data.     

Estimation of pore‐pressure change in a compacting reservoir from time‐lapse seismic data

An approach is developed to estimate pore‐pressure changes in a compacting chalk reservoir directly from time‐lapse seismic attributes. It is applied to data from the south‐east flank of the Valhall field. The time‐lapse seismic signal of the reservoir in this area is complex, despite the fact that saturation changes do not have an influence. This complexity reflects a combination of pressure depletion, compaction and stress re‐distribution throughout the reservoir and into the surrounding rocks. A simple relation is found to link the time‐lapse amplitude and time‐shift attributes to variations in the key controlling parameter of initial porosity. This relation is sufficient for an accurate estimation of pore‐pressure change in the inter‐well space. Although the time‐lapse seismic estimates mostly agree with reservoir simulation, unexplained mismatches are apparent at a small number of locations with lower porosities (less than 38%). The areas of difference between the observations and predictions suggest possibilities for simulation model updating or a better understanding of the physics of the reservoir.     

Seismic attenuation and velocity dispersion in fractured rocks: The role played by fracture contact areas

The presence of fractures in fluid‐saturated porous rocks is usually associated with strong seismic P‐wave attenuation and velocity dispersion. This energy dissipation can be caused by oscillatory wave‐induced fluid pressure diffusion between the fractures and the host rock, an intrinsic attenuation mechanism generally referred to as wave‐induced fluid flow. Geological observations suggest that fracture surfaces are highly irregular at the millimetre and sub‐millimetre scale, which finds its expression in geometrical and mechanical complexities of the contact area between the fracture faces. It is well known that contact areas strongly affect the overall mechanical fracture properties. However, existing models for seismic attenuation and velocity dispersion in fractured rocks neglect this complexity. In this work, we explore the effects of fracture contact areas on seismic P‐wave attenuation and velocity dispersion using oscillatory relaxation simulations based on quasi‐static poroelastic equations. We verify that the geometrical and mechanical details of fracture contact areas have a strong impact on seismic signatures. In addition, our numerical approach allows us to quantify the vertical solid displacement jump across fractures, the key quantity in the linear slip theory. We find that the displacement jump is strongly affected by the geometrical details of the fracture contact area and, due to the oscillatory fluid pressure diffusion process, is complex‐valued and frequency‐dependent. By using laboratory measurements of stress‐induced changes in the fracture contact area, we relate seismic attenuation and dispersion to the effective stress. The corresponding results do indeed indicate that seismic attenuation and phase velocity may constitute useful attributes to constrain the effective stress. Alternatively, knowledge of the effective stress may help to identify the regions in which wave induced fluid flow is expected to be the dominant attenuation mechanism.     

An approach to combined rock physics and seismic modelling of fluid substitution effects

The aim of seismic reservoir monitoring is to map the spatial and temporal distributions and contact interfaces of various hydrocarbon fluids and water within a reservoir rock. During the production of hydrocarbons, the fluids produced are generally displaced by an injection fluid. We discuss possible seismic effects which may occur when the pore volume contains two or more fluids. In particular, we investigate the effect of immiscible pore fluids, i.e. when the pore fluids occupy different parts of the pore volume. The modelling of seismic velocities is performed using a differential effective‐medium theory in which the various pore fluids are allowed to occupy the pore space in different ways. The P‐wave velocity is seen to depend strongly on the bulk modulus of the pore fluids in the most compliant (low aspect ratio) pores. Various scenarios of the microscopic fluid distribution across a gas–oil contact (GOC) zone have been designed, and the corresponding seismic properties modelled. Such GOC transition zones generally give diffuse reflection regions instead of the typical distinct GOC interface. Hence, such transition zones generally should be modelled by finite‐difference or finite‐element techniques. We have combined rock physics modelling and seismic modelling to simulate the seismic responses of some gas–oil zones, applying various fluid‐distribution models. The seismic responses may vary both in the reflection time, amplitude and phase characteristics. Our results indicate that when performing a reservoir monitoring experiment, erroneous conclusions about a GOC movement may be drawn if the microscopic fluid‐distribution effects are neglected.     

水库蓄放水对库底岩石介质弹性波速影响的数值模拟

为了解水库水体加、卸载及渗透过程中,库底岩石介质有效应力变化对弹性波速的影响,以及弹性波速变化与孔隙压力、有效应力变化之间的定量关系,以四川省紫坪铺水库为例,在前期已建立库区地质构造与水文地质结构模型,并推导出岩石介质变形与流体渗流耦合数学模型的基础上,进一步建立了有效应力对岩石弹性波速影响的数学模型,利用有限元方法定量计算了库底岩石介质的孔隙压力、附加有效应力和弹性波速的变化。结果表明:在水库水体加、卸载及渗透过程中,地下岩石介质弹性波速增量值的变化并不明显,最大变幅仅为±0.013km/s,变化范围主要集中在库底5km以上的局部区域;弹性波速增量值与附加有效应力变化同步,与水库水位变化形态相似;不同观测点弹性波速变化量的大小与埋藏位置、深度及附加有效应力的变化幅度有关,同一观测点,弹性纵波波速变化幅度大于弹性横波波速。文中数值模拟的结果与一些学者通过环境噪声方法获得的紫坪铺水库附近区域相对波速变化的反演结果在变化形态上大体一致,但变化幅度略有差异。     

水域隧道地震响应分析

本文基于Biot动力固结理论和弹性动力学理论,考虑海床（土壤）的两相性、黏弹性人工边界及流（水）-固耦合作用,建立了隧道-土-流体相互作用的力学模型,讨论了P波作用下有无水的情况以及水深、水域隧道埋深、海床土性质和地震波入射角等因素对隧道及其周围海床应力的影响。结果表明:隧道周围海床土的孔隙水压力和隧道内应力随着水深的增加而增加;地震波特性和海床土特性对隧道的内应力和海床土的孔隙水压力均有较大的影响;海床土的渗透性和隧道埋深对隧道的内应力影响较小,而对隧道周围海床土的孔隙水压力影响较大;地震动的入射角对隧道的内应力和隧道附近土层的孔隙水压力均有较大影响。      

Explicit use of the Biot coefficient in predicting shear-wave velocity of water-saturated sediments

Predicting the shear‐wave (S‐wave) velocity is important in seismic modelling, amplitude analysis with offset, and other exploration and engineering applications. Under the low‐frequency approximation, the classical Biot–Gassmann theory relates the Biot coefficient to the bulk modulus of water‐saturated sediments. If the Biot coefficient under in situ conditions can be estimated, the shear modulus or the S‐wave velocity can be calculated. The Biot coefficient derived from the compressional‐wave (P‐wave) velocity of water‐saturated sediments often differs from and is less than that estimated from the S‐wave velocity, owing to the interactions between the pore fluid and the grain contacts. By correcting the Biot coefficients derived from P‐wave velocities of water‐saturated sediments measured at various differential pressures, an accurate method of predicting S‐wave velocities is proposed. Numerical results indicate that the predicted S‐wave velocities for consolidated and unconsolidated sediments agree well with measured velocities.     

Joint cross-well and single-well seismic studies of CO2 injection in an oil reservoir

A series of time‐lapse seismic cross‐well and single‐well experiments were conducted in a diatomite reservoir to monitor the injection of CO₂ into a hydrofracture zone, based on P‐ and S‐wave data. A high‐frequency piezo‐electric P‐wave source and an orbital‐vibrator S‐wave source were used to generate waves that were recorded by hydrophones as well as 3‐component geophones. During the first phase the set of seismic experiments was conducted after the injection of water into the hydrofractured zone. The set of seismic experiments was repeated after a time period of seven months during which CO₂ was injected into the hydrofractured zone. The questions to be answered ranged from the detectability of the geological structure in the diatomic reservoir to the detectability of CO₂ within the hydrofracture. Furthermore, it was intended to determine which experiment (cross‐well or single‐well) is best suited to resolve these features. During the pre‐injection experiment, the P‐wave velocities exhibited relatively low values between 1700 and 1900 m/s, which decreased to 1600–1800 m/s during the post‐injection phase (?5%). The analysis of the pre‐injection S‐wave data revealed slow S‐wave velocities between 600 and 800 m/s, while the post‐injection data revealed velocities between 500 and 700 m/s (?6%). These velocity estimates produced high Poisson's ratios between 0.36 and 0.46 for this highly porous (～50%) material. Differencing post‐ and pre‐injection data revealed an increase in Poisson's ratio of up to 5%. Both velocity and Poisson's ratio estimates indicate the dissolution of CO₂ in the liquid phase of the reservoir accompanied by an increase in pore pressure. The single‐well data supported the findings of the cross‐well experiments. P‐ and S‐wave velocities as well as Poisson's ratios were comparable to the estimates of the cross‐well data. The cross‐well experiment did not detect the presence of the hydrofracture but appeared to be sensitive to overall changes in the reservoir and possibly the presence of a fault. In contrast, the single‐well reflection data revealed an arrival that could indicate the presence of the hydrofracture between the source and receiver wells, while it did not detect the presence of the fault, possibly due to out‐of‐plane reflections.     

Research Note: Overpressure prediction from C‐wave seismic data

Recently, mode converted shear waves (C‐waves) have been shown to enable overpressure prediction in media where primary wave acquisition is inhibited by gas and fluid effects – C‐wave moveout is analysed and a long standing relationship between differential stress and primary‐wave (P‐wave) velocity is modified and employed. Though pore‐pressure prediction based on C‐waves is supported by empirical evidence from laboratory and field experiments, a theoretical justification has yet to be developed. In this research note, we provide a supporting algebra for the original relationship between pore pressure and C‐wave velocity.     

粤闽赣交界区波速比特征研究

根据多台和达法,利用广东、福建、江西三省数字地震观测记录对粤闽赣交界区及邻区波速比特征进行研究,获取了具有参考价值的结果：粤闽赣交界地区沿海一侧明显比内陆地区波速比要高;约在北纬24°,东经114°处,处走向北东方向上是波速变化比较明显的分界线,该分界线可能是由于地下两侧的岩石岩性不同造成的,或与该地区介质物理性质和化学性质存在变异关有,也可能与此地区地震应力场变化有一定关系。     

The effect of clay distribution on the elastic properties of sandstones

The shape and location of clay within sandstones have a large impact on the P‐wave and S‐wave velocities of the rock. They also have a large effect on reservoir properties and the interpretation of those properties from seismic data and well logs. Numerical models of different distributions of clay – structural, laminar and dispersed clay – can lead to an understanding of these effects. Clay which is located between quartz grains, structural clay, will reduce the P‐wave and S‐wave velocities of the rock. If the clay particles become aligned or form layers, the velocities perpendicular to the alignment will be reduced further. S‐wave velocities decrease more rapidly than P‐wave velocities with increasing clay content, and therefore Poisson's ratios will increase as the velocities decrease. These effects are more pronounced for compacted sandstones. Small amounts of clay that are located in the pore space will have little effect on the P‐wave velocity due to the competing influence of the density effect and pore‐fluid stiffening. The S‐wave velocity will decrease due to the density effect and thus the Poisson's ratio will increase. When there is sufficient clay to bridge the gaps between the quartz grains, P‐wave and S‐wave velocities rise rapidly and the Poisson's ratios decrease. These effects are more pronounced for under‐compacted sandstones. These general results are only slightly modified when the intrinsic anisotropy of the clay material is taken into account. Numerical models indicate that there is a strong, nearly linear relationship between P‐wave and S‐wave velocity which is almost independent of clay distribution. S‐wave velocities can be predicted reasonably accurately from P‐wave velocities based on empirical relationships. However, this does not provide any connection between the elastic and petrophysical properties of the rocks. Numerical modelling offers this connection but requires the inclusion of clay distribution and anisotropy to provide a model that is consistent with both the elastic and petrophysical properties. If clay distribution is ignored, predicting porosities from P‐wave or S‐wave data, for example, can result in large errors. Estimation of the clay distribution from P‐wave and S‐wave velocities requires good estimates of the porosity and clay volume and verification from petrographic analyses of core or cuttings. For a real data example, numerical models of the elastic properties suggest the predominance of dispersed clay in a fluvial sand from matching P‐wave and S‐wave velocity well log data using log‐based estimates of the clay volume and porosity. This is consistent with an interpretation of other log data.     

对扶余油田套管变形的几点看法

我们利用扶余油田的压裂资料,分析了该油田应力场的特点,探讨了油田套管变形的原因.认为该区以水平压应力作用为主.由于高压注水,有效法向应力降低,引起地层间的相对滑动,造成套管变形.主要的套管变形是由于地层沿水平间断面--AB 界面的滑动造成的.通过控制注入压力和注水方式可以降低 AB 界面中的空隙压力,使界面上的法向应力有所恢复,降低套管变形的速率.      

When 4D seismic is not applicable: Alternative monitoring scenarios for the Arab-D reservoir in the Ghawar Field

Ghawar, the largest oilfield in the world, produces oil from the Upper Jurassic Arab‐D carbonate reservoir. The high rigidity of the limestone–dolomite reservoir rock matrix and the small contrast between the elastic properties of the pore fluids, i.e. oil and water, are responsible for the weak 4D seismic effect due to oil production. A feasibility study was recently completed to quantify the 4D seismic response of reservoir saturation changes as brine replaced oil. The study consisted of analysing reservoir rock physics, petro‐acoustic data and seismic modelling. A seismic model of flow simulation using fluid substitution concluded that time‐lapse surface seismic or conventional 4D seismic is unlikely to detect the floodfront within the repeatability of surface seismic measurements. Thus, an alternative approach to 4D seismic for reservoir fluid monitoring is proposed. Permanent seismic sensors could be installed in a borehole and on the surface for passive monitoring of microseismic activity from reservoir pore‐pressure perturbations. Reservoir production and injection operations create these pressure or stress perturbations. Reservoir heterogeneities affecting the fluid flow could be mapped by recording the distribution of epicentre locations of these microseisms or small earthquakes. The permanent borehole sensors could also record repeated offset vertical seismic profiling surveys using a surface source at a fixed location to ensure repeatability. The repeated vertical seismic profiling could image the change in reservoir properties with production.     

含不同孔隙流体的砂岩地震波速度随压力变化的实验研究

岩石的地震波性质是区域构造研究和浅部地震勘探应用的基础.延长油田是我国重要的油气生产基地之一,但目前仍缺乏地震波性质方面的基础资料.作者利用Autolab2000多功能岩石物性自动测试设备,在0~180MPa及饱含不同孔隙流体(干燥、饱水及饱油)条件下,研究了三种来自延长油田砂岩岩芯的纵波、横波速度.结果表明:三种砂岩的V_p、V_s1和V_s2均随压力增加(或降低)而基本呈对数曲线增大(或减小);干燥、饱水和饱油三种波速间的关系因砂岩类型不同而不同,这主要取决于岩石的有效弹性模量、孔隙流体性质以及岩石的内部结构等;含同种孔隙流体的不同类型砂岩,其V_p、V_s1和V_s2随压力变化的规律主要受岩石孔隙度和粒度的影响;而含不同孔隙流体的同种砂岩,其V_p、V_s1和V_s2随压力变化的规律则主要受控于岩石的有效弹性模量和流体密度.另外,含水或含油饱和度的变化对V_s1和V_s2基本没有影响.实验结果可以为该地区地震资料的解释及与声波测井之间的对比提供重要的基础数据和参考依据.     

Analysis of time‐lapse travel‐time and amplitude changes to assess reservoir compartmentalization

Fluid depletion within a compacting reservoir can lead to significant stress and strain changes and potentially severe geomechanical issues, both inside and outside the reservoir. We extend previous research of time‐lapse seismic interpretation by incorporating synthetic near‐offset and full‐offset common‐midpoint reflection data using anisotropic ray tracing to investigate uncertainties in time‐lapse seismic observations. The time‐lapse seismic simulations use dynamic elasticity models built from hydro‐geomechanical simulation output and a stress‐dependent rock physics model. The reservoir model is a conceptual two‐fault graben reservoir, where we allow the fault fluid‐flow transmissibility to vary from high to low to simulate non‐compartmentalized and compartmentalized reservoirs, respectively. The results indicate time‐lapse seismic amplitude changes and travel‐time shifts can be used to qualitatively identify reservoir compartmentalization. Due to the high repeatability and good quality of the time‐lapse synthetic dataset, the estimated travel‐time shifts and amplitude changes for near‐offset data match the true model subsurface changes with minimal errors. A 1D velocity–strain relation was used to estimate the vertical velocity change for the reservoir bottom interface by applying zero‐offset time shifts from both the near‐offset and full‐offset measurements. For near‐offset data, the estimated P‐wave velocity changes were within 10% of the true value. However, for full‐offset data, time‐lapse attributes are quantitatively reliable using standard time‐lapse seismic methods when an updated velocity model is used rather than the baseline model.