Bayesian inversion of time‐lapse seismic data for the estimation of static reservoir properties and dynamic property changes

Seismic conditioning of static reservoir model properties such as porosity and lithology has traditionally been faced as a solution of an inverse problem. Dynamic reservoir model properties have been constrained by time‐lapse seismic data. Here, we propose a methodology to jointly estimate rock properties (such as porosity) and dynamic property changes (such as pressure and saturation changes) from time‐lapse seismic data. The methodology is based on a full Bayesian approach to seismic inversion and can be divided into two steps. First we estimate the conditional probability of elastic properties and their relative changes; then we estimate the posterior probability of rock properties and dynamic property changes. We apply the proposed methodology to a synthetic reservoir study where we have created a synthetic seismic survey for a real dynamic reservoir model including pre‐production and production scenarios. The final result is a set of point‐wise probability distributions that allow us to predict the most probable reservoir models at each time step and to evaluate the associated uncertainty. Finally we also show an application to real field data from the Norwegian Sea, where we estimate changes in gas saturation and pressure from time‐lapse seismic amplitude differences. The inverted results show the hydrocarbon displacement at the times of two repeated seismic surveys.     

有效压力与饱和度变化的气藏多波时移地震AVO响应

天然气在开发过程中,储层有效压力和含气饱和度均会发生变化,研究有效压力和含气饱和度的变化对地震响应特征的影响,在基于时移地震的剩余气分布预测研究中具有重要意义。天然气和石油的声学性质有着明显的差异,油藏时移地震的研究成果不能直接应用于气藏,因此需要开展气藏的时移地震研究。利用Shapiro模型表征干岩石弹性模量随有效压力的变化,借助Batzle-Wang方程描述流体速度随压力的变化关系,联合Gassmann理论进行流体替代,表征饱和流体岩石速度随含气饱和度的变化,建立了饱和流体岩石速度随有效压力和饱和度变化的岩石物理模型。基于该模型,对不同含气饱和度和不同有效压力下的气藏储层模型进行了多波时移地震叠前振幅变化（AVO）模拟。结果表明多波时移地震AVO技术可以有效地区分有效压力变化和含气饱和度变化,为进一步开展气藏多波时移地震流体监测提供了理论参考依据。      

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.     

Optimal use of PP and PS time-lapse stacks for fluid–pressure discrimination

The combined use of time‐lapse PP and PS seismic data is analysed for optimal discrimination between pressure and saturation changes. The theory is based on a combination of the well‐known Gassmann model and the geomechanical grain model derived by Hertz and Mindlin. A key parameter in the discrimination process is the opening angle between curves representing constant changes in PP and PS reflectivity plotted against pressure and saturation changes. The optimal discrimination angle in the pressure–saturation space is 90° and this is used to determine optimal offset ranges for both PP and PS data. For typical production scenarios, we find an optimal offset range corresponding to an angle of incidence of 25–30°, for both PP and PS data. For gas we find slightly different results. This means that conventional survey parameters used in marine multicomponent acquisition should be sufficient for the purpose of estimating pressure and fluid saturation changes during production.     

Quantitative detection of fluid distribution using time-lapse seismic

Although previous seismic monitoring studies have revealed several relationships between seismic responses and changes in reservoir rock properties, the quantitative evaluation of time‐lapse seismic data remains a challenge. In most cases of time‐lapse seismic analysis, fluid and/or pressure changes are detected qualitatively by changes in amplitude strength, traveltime and/or Poisson's ratio. We present the steps for time‐lapse seismic analysis, considering the pressure effect and the saturation scale of fluids. We then demonstrate a deterministic workflow for computing the fluid saturation in a reservoir in order to evaluate time‐lapse seismic data. In this approach, we derive the physical properties of the water‐saturated sandstone reservoir, based on the following inputs: V_P, V_S, ρ and the shale volume from seismic analysis, the average properties of sand grains, and formation‐water properties. Next, by comparing the in‐situ fluid‐saturated properties with the 100% formation‐water‐saturated reservoir properties, we determine the bulk modulus and density of the in‐situ fluid. Solving three simultaneous equations (relating the saturations of water, oil and gas in terms of the bulk modulus, density and the total saturation), we compute the saturation of each fluid. We use a real time‐lapse seismic data set from an oilfield in the North Sea for a case study.     

Extraction of permeability from time-lapse seismic data

Two formulae are developed for estimating horizontal permeability directly from maps of 4D seismic signatures. The choice of the formula used depends on whether the seismic is dominated by changes of pressure or saturation. However, pressure derived from time‐lapse seismic, or seismic amplitudes controlled predominantly by pressure are to be preferred for optimal ‘illumination’ of the reservoir. The permeability is predicted to be dependent on porosity but weighted by a 4D term related to the magnitude and spatial gradient of the 4D signature. Tests performed on model‐based synthetic seismic data affirm the validity and accuracy of this approach. Application to field data from the UK continental shelf reveals a large‐scale permeability variation similar to the existing simulation model, but with additional fine‐scale detail. The technique thus has the potential of providing extra information with which to update the simulation model. The resultant permeability estimates have been successfully ground‐truthed against the results of two well tests. As non‐repeatable noise in the time‐lapse seismic data diminishes with improved 4D‐related acquisition, it will become increasingly possible to make robust permeability estimates using this approach.     

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.     

多波时移地震AVO反演研究

数值模拟了油藏含油饱和度与有效压力变化时移地震AVO的响应,确定利用时移地震AVO区分油藏参数的变化、实现油藏定量解释的可行性.从Aki等 AVO近似方程出发,详细推导了P_P波和P_S转换波时移地震AVO计算公式.结合岩石物理近似关系和本文推导的时移地震AVO计算公式,推导了利用多波时移地震AVO反演油藏含油饱和度和压力变化的方程.数据试验表明,文中推导的多波时移地震AVO方程能较好地反演油藏含油饱和度变化和有效压力变化,实现油藏定量解释.     

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.     

Error in shear-wave polarization and time splitting

Shear‐wave polarization and time delay are attributes commonly used for fracture detection and characterization. In time‐lapse analysis these parameters can be used as indicators of changes in the fracture orientation and density. Indeed, changes in fracture characteristics provide key information for increased reservoir characterization and exploitation. However, relative to the data uncertainty, is the comparison of these parameters over time statistically meaningful? We present the uncertainty in shear‐wave polarization and time delay as a function of acquisition uncertainties, such as receiver and source misorientation, miscoupling and band‐limited random noise. This study is applied to a time‐lapse borehole seismic survey, recorded in Vacuum Field, New Mexico. From the estimated uncertainties for each survey, the uncertainty in the difference between the two surveys is 31° for the shear‐wave polarization angle and 4 ms for the shear‐wave time delay. Any changes in these parameters greater than these error estimates can be interpreted with confidence. This analysis can be applied to any time‐lapse measurement to provide an interval of confidence in the interpretation of shear‐wave polarization angles and time splitting.     

Going quantitative with 4D seismic analysis

It is demonstrated that time‐lapse seismic signatures can be directly calibrated with historical data from producing and injecting wells via a reservoir simulator, material balance calculation or simply using the hard data. When this procedure is applied to a field over which two or more repeat surveys have been shot at different calendar times, the correlation coefficients that link the seismic difference signatures to the reservoir's pressure and saturation variations are determined. By utilizing several seismic attributes that respond differently to reservoir perturbations, pressure and saturation changes are then independently estimated. The approach is tested on synthetic data and then on data from the Schiehallion Field on the UK continental shelf, with favourable results.     

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.     

砂岩储层AVO特征影响因素的不确定性研究

传统的地震AVO正演研究多采用参数固定的岩石物理模型,而实际地层属性参数在勘探范围内具有不确定性.本研究以目标地层岩芯样品的实验室测试数据为基础,通过样品孔隙度和干燥状态下纵、横波阻抗的高度线性关系对岩石物理模型进行了简化,并结合实验测量和测井解释建立了主要模型参数的概率密度函数.采用Monte-Carlo随机正演和G...     

Study on attribute characterization for reservoir dynamic monitoring by seismic

Study on characterizing reservoir parameters dynamic variations by time-lapse seismic attributes is the theoretical basis for effectively distinguishing reservoir parameters variations and conducting time-lapse seismic interpretation,and it is also a key step for time-lapse seismic application in real oil fields. Based on the rock physical model of unconsolidated sandstone,the different effects of oil saturation and effective pressure variations on seismic P-wave and S-wave velocities are calculated and analyzed. Using numerical simulation on decoupled wave equations,the responses of seismic amplitude with different offsets to reservoir oil saturation variations are analyzed,pre-stack time-lapse seismic attributes differences for oil saturation and effective pressure variations of P-P wave and P-S converted wave are calculated,and time-lapse seismic AVO (Amplitude Versus Offset) response rules of P-P wave and P-S converted wave to effective pressure and oil saturation variations are compared. The theoretical modeling study shows that it is feasible to distinguish different reservoir parameters dynamic variations by pre-stack time-lapse seismic information,including pre-stack time-lapse seismic attributes and AVO information,which has great potential in improving time-lapse seismic interpreta-tion precision. It also shows that the time-lapse seismic response mechanism study on objective oil fields is especially important in establishing effective time-lapse seismic data process and interpreta-tion scheme.     

Sub‐sample time shift and horizontal displacement measurements using phase‐correlation method in time‐lapse seismic

Hydrocarbon production and fluid injection affect the level of subsurface stress and physical properties of the subsurface, and can cause reservoir‐related issues, such as compaction and subsidence. Monitoring of oil and gas reservoirs is therefore crucial. Time‐lapse seismic is used to monitor reservoirs and provide evidence of saturation and pressure changes within the reservoir. However, relative to background velocities and reflector depths, the time‐lapse changes in velocity and geomechanical properties are typically small between consecutive surveys. These changes can be measured by using apparent displacement between migrated images obtained from recorded data of multiple time‐lapse surveys. Apparent displacement measurements by using the classical cross‐correlation method are poorly resolved. Here, we propose the use of a phase‐correlation method, which has been developed in satellite imaging for sub‐pixel registration of the images, to overcome the limitations of cross‐correlation. Phase correlation provides both vertical and horizontal displacements with a much better resolution. After testing the method on synthetic data, we apply it to a real dataset from the Norne oil field and show that the phase‐correlation method can indeed provide better resolution.     

Seismic time‐lapse effects of solution salt mining – a feasibility study

This article addresses the question whether time‐lapse seismic reflection techniques can be used to follow and quantify the effects of solution salt mining. Specifically, the production of magnesium salts as mined in the north of the Netherlands is considered. The use of seismic time‐lapse techniques to follow such a production has not previously been investigated. For hydrocarbon production and CO₂ storage, time‐lapse seismics are used to look at reservoir changes mainly caused by pressure and saturation changes in large reservoirs, while for solution mining salt is produced from caverns with a limited lateral extent, with much smaller production volumes and a fluid (brine) replacing a solid (magnesium salt). In our approach we start from the present situation of the mine and then study three different production scenarios, representing salt production both in vertical and lateral directions of the mine. The present situation and future scenarios have been transformed into subsurface models that were input to an elastic finite‐difference scheme to create synthetic seismic data. These data have been analysed and processed up to migrated seismic images, such that time‐lapse analyses of intermediate and final results could be done. From the analyses, it is found that both vertical and lateral production is visible well above the detection threshold in difference data, both at pre‐imaging and post‐imaging stages. In quantitative terms, an additional production of the mine of 6 m causes time‐shifts in the order of 2 ms (pre‐imaging) and 4 ms (post‐imaging) and amplitude changes of above 20% in the imaged sections. A laterally oriented production causes even larger amplitude changes at the edge of the cavern due to replacement of solid magnesium salt with brine introducing a large seismic contrast. Overall, our pre‐imaging and post‐imaging time‐lapse analysis indicates that the effects of solution salt mining can be observed and quantified on seismic data. The effects seem large enough to be observable in real seismic data containing noise.     

Integrating gravimetric and interferometric synthetic aperture radar data for enhancing reservoir history matching of carbonate gas and volatile oil reservoirs

Reservoir history matching is assuming a critical role in understanding reservoir characteristics, tracking water fronts, and forecasting production. While production data have been incorporated for matching reservoir production levels and estimating critical reservoir parameters, the sparse spatial nature of this dataset limits the efficiency of the history matching process. Recently, gravimetry techniques have significantly advanced to the point of providing measurement accuracy in the microgal range and consequently can be used for the tracking of gas displacement caused by water influx. While gravity measurements provide information on subsurface density changes, i.e., the composition of the reservoir, these data do only yield marginal information about temporal displacements of oil and inflowing water. We propose to complement gravimetric data with interferometric synthetic aperture radar surface deformation data to exploit the strong pressure deformation relationship for enhancing fluid flow direction forecasts. We have developed an ensemble Kalman‐filter‐based history matching framework for gas, gas condensate, and volatile oil reservoirs, which synergizes time‐lapse gravity and interferometric synthetic aperture radar data for improved reservoir management and reservoir forecasts. Based on a dual state–parameter estimation algorithm separating the estimation of static reservoir parameters from the dynamic reservoir parameters, our numerical experiments demonstrate that history matching gravity measurements allow monitoring the density changes caused by oil–gas phase transition and water influx to determine the saturation levels, whereas the interferometric synthetic aperture radar measurements help to improve the forecasts of hydrocarbon production and water displacement directions. The reservoir estimates resulting from the dual filtering scheme are on average 20%–40% better than those from the joint estimation scheme, but require about a 30% increase in computational cost.     

Utilizing spectral decomposition to determine the distribution of injected CO2 at the Snøhvit Field

Time‐lapse 3D seismic reflection data, covering the CO₂ storage operation at the Snøhvit gas field in the Barents Sea, show clear amplitude and time‐delay differences following injection. The nature and extent of these changes suggest that increased pore fluid pressure contributes to the observed seismic response, in addition to a saturation effect. Spectral decomposition using the smoothed pseudo‐Wigner–Ville distribution has been used to derive discrete‐frequency reflection amplitudes from around the base of the CO₂ storage reservoir. These are utilized to determine the lateral variation in peak tuning frequency across the seismic anomaly as this provides a direct proxy for the thickness of the causative feature. Under the assumption that the lateral and vertical extents of the respective saturation and pressure changes following CO₂ injection will be significantly different, discrete spectral amplitudes are used to distinguish between the two effects. A clear spatial separation is observed in the distribution of low‐ and high‐frequency tuning. This is used to discriminate between direct fluid substitution of CO₂, as a thin layer, and pressure changes that are distributed across a greater thickness of the storage reservoir. The results reveal a striking correlation with findings derived from pressure and saturation discrimination algorithms based on amplitude versus offset analysis.     

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.     

Seismic monitoring of pressure depletion evaluated for a United Kingdom continental-shelf gas reservoir

The possibility of using 4D seismic data for monitoring pressure depletion in the low‐porosity, tight gas‐bearing Rotliegende sandstones of the UK Southern Gas Basin is investigated. The focus here is on whether fractures in the upper part of the reservoir, known to enhance productivity, can also enhance the time‐lapse seismic response. The study uses laboratory data to evaluate core‐plug stress sensitivity, published data for the stress behaviour of the fractures, followed by petro‐elastic and 4D seismic modelling of both the fractured and unfractured formation. The magnitude of the resultant 4D signatures suggests that production‐induced changes in the unfractured sands are unlikely to be observed except perhaps with highly repeatable time‐lapse surveys. On the other hand, the presence of fractures could render production effects visible in dedicated 4D acquisition or prestack parallel processed data. If present however, the signature will be sporadic, as fractures in the area are known to exist in clusters. The 4D signature may be enhanced further by certain classes of vertical geological variability and also areas of high reservoir pressure. The strongest evidence of depletion is expected to be time‐shifts seen at the base of the Rotliegende reservoir.