Time-dependent Inversion of Surface Subsidence due to Dynamic Reservoir Compaction

We introduce a novel, time-dependent inversion scheme for resolving temporal reservoir pressure drop from surface subsidence observations (from leveling or GPS data, InSAR, tiltmeter monitoring) in a single procedure. The theory is able to accommodate both the absence of surface subsidence estimates at sites at one or more epochs as well as the introduction of new sites at any arbitrary epoch. Thus, all observation sites with measurements from at least two epochs are utilized. The method uses both the prior model covariance matrix and the data covariance matrix, which incorporates the spatial and temporal correlations between model parameters and data, respectively. The incorporation of the model covariance implicitly guarantees smoothness of the model estimate, while maintaining specific geological features like sharp boundaries. Taking these relations into account through the model covariance matrix enhances the influence of the data on the inverted model estimate. This leads to a better defined and interpretable model estimate. The time-dependent aspect of the method yields a better constrained model estimate and makes it possible to identify non-linear acceleration or delay in reservoir compaction. The method is validated by a synthetic case study based on an existing gas reservoir with a highly variable transmissibility at the free water level. The prior model covariance matrix is based on a Monte Carlo simulation of the geological uncertainty in the transmissibility.     

Disentangling Shallow and Deep Processes Causing Surface Movement

Understanding and predicting surface movement is important both technically and for social reasons. The shallow processes contributing to subsidence include construction works, peat oxidation, clay compaction, and groundwater withdrawal; deep causes are hydrocarbon and salt production. We describe an inversion procedure we have devised to disentangle the deep and shallow causes of surface movement. It employs a Bayesian inversion scheme, using forward models and other ‘a priori’ information about shallow and deep compaction. Parameter estimation thus takes place at two different depths, thereby disentangling the deep and shallow compaction processes responsible for surface movement. The uncertainty in the surface measurements and ‘a priori’ estimates is naturally incorporated. Furthermore, spatial and temporal correlations can be taken into account through inclusion of the covariance matrix. The inversion scheme is demonstrated for two synthetic cases. The first combines a compacting gas field and a compacting shallow peat layer. We demonstrate that assumptions on the shape of the subsidence bowl are not necessary. We also show how neglecting either deep or shallow causes of subsidence can produce spurious results. The advantage of using the ‘a priori’ estimates of the compaction and the covariance matrix obtained by Monte Carlo simulations is demonstrated with a second synthetic example involving two polders and different depths of their water table. A robust solution is obtained for each polder unit, while a simpler (and faster) ‘a priori’ estimate based on the expected average clay thickness fails to reproduce the actual compaction. Monte Carlo simulations can also be applied to compaction in depleting gas reservoirs. Information on spatial correlations is often available, even when the absolute values of the ‘a priori’ compaction data are quite uncertain. Explicitly incorporating such ‘a priori’ known spatial correlations improves the result significantly.     

碳酸盐岩礁滩油气储层地震预测方法探讨

储层结构和孔隙流体预测是目前碳酸盐岩礁滩油气储层地震预测的重点和难点。这里从流体敏感性参数的选择和基于储层结构模拟的孔隙度预测二方面。研究了碳酸盐岩礁滩油气储层的流体识别问题。其中,基于测井资料统计分析和／或岩石物理岩样测试的参数交会图的制作,是优选烃类敏感参数的基础。在单一敏感参数的基础上,构组复合型的流体识别因子,能获得更好的流体识别效果。储层孔隙度预测是这样实现的：首先,对Gassman流体替换方程通过引入近似关系βp-βs≈βp进行简化;然后引入Eshelby—Walsh储层结构参数以获得直接计算孔隙度的表达式;最后,根据弹性反演得到的纵波、横渡阻抗（或纵波、横波速度）等参数,计算得到孔隙度及孔隙流体预测剖面。经实际地震资料的流体预测结果显示,新方法比常规方法预测的精度高。     

含水层压密引起其特征参数变化的实验

水文地质参数在含水层压密过程中不断变化,这是诸多地面沉降模型实际应用中的难点之一。就含水层压密对水文地质参数的影响开展了初步的实验,结果表明,压密前后含水层的渗透系数和给水度发生了较大的变化。其中：渗透系数随模拟含水层介质压密过程的变化几乎呈线性的减小趋势,线性拟合决定系数为0.959 2~0.997 1;给水度随着含水层的压实而表现出下降的趋势较为复杂,随介质类型的不同而有差异。渗透系数和给水度的下降速度在不同介质中也有一定的差异。在本研究的实验模型尺度下,给水度和渗透系数呈现一定的线性正相关关系,一次线性相关函数斜率为0.001 3~0.005 1,截距为0.011 6~0.038 1,基本相近且在相同数量级。     

Fully coupled modeling of seabed subsidence and reservoir compaction of North Sea oil fields

This paper focuses on the aspects of fully coupled continuum modeling of multiphase poroelasticity applied to the three-dimensional numerical simulations of the Ekofisk oil reservoir in the North Sea (56°29′–34′N, 03°10′–14′E). A systematic presentation is chosen to present the methodology behind fully coupled, continuum modeling. First, a historical review of the subsidence phenomena above an oil and gas reservoir is given. This will serve as a background against which the relevance of the present approach to compaction and subsidence modeling will be demonstrated. Following this, the governing equations for a multiphase poroelasticity model are briefly presented. Particular attention is paid to the analysis of the pore-compressibility term usually used in an uncoupled approach for characterising the host-rock deformation. A comparative numerical analysis is carried out to contrast and highlight the difference between coupled and uncoupled reservoir simulators. Finally, a finite-element numerical model of the Ekofisk field is presented and a significant result is a contour map of seabed subsidence which is in general agreement with the shape of the subsidence contours based on past bathymetric surveys. Analysis of the simulation reveals that, due to the downward movement of the overburden, oil migration occurs from the crest of the anticline in which the field is situated, towards the flank. The pore-pressure depletion in the reservoir is significantly delayed due to the replenishment of the reservoir energy via the formational compaction. Horizontal movement in the reservoir, which is neglected in traditional modeling, can be significant and comparable in magnitude to the vertical subsidence. Electronic Publication     

石油开采引起的油藏压实与地面沉陷预测

石油开采过程中的油藏压实和地面沉陷是海上油田开发不容忽视的问题。通过对油藏压实与沉陷的机理及影响因素分析,给出了油藏压实与沉陷量的预测模型及计算方法,并以某海上油藏实例进行了计算。对于油藏开发整体规划、海上作业平台优化设计有一定的指导意义。     

塔河油田3区石炭系超深薄层碎屑岩储层预测研究

针对塔河油田3区石炭系卡拉沙依组地震数据很难识别薄砂体的问题,对比分析了采用地震资料提频处理、分频处理、储层高分辨率敏感参数反演等不同手段得到的储层预测结果,筛选出高分辨率储层敏感参数反演作为卡拉沙依组砂泥岩段储层主要预测手段。通过探讨砂泥岩对声波时差的响应,以及对比分析自然电位、自然伽马以及补偿中子孔隙度与声波时差的关系,确定自然电位与声波时差的相关性最好,由此选取自然电位作为最佳电性敏感参数参与高分辨率敏感参数反演预测。从井点、剖面、平面等方面检验和评价高分辨率储层预测成果,结果表明其反演预测效果较好,符合塔河油田3区石炭系的储层预测要求,实现了对石炭系主力砂体空间展布的解释与描述,建立了塔河油田3区石炭系卡拉沙依组储层模型。     

叠前反演方法在致密砂岩气储层预测中的应用

以鄂尔多斯东缘A区块为例,通过岩石物理正演分析,论证了储层岩石物理参数的敏感性,确定利用纵波阻抗与纵横波速度比参数进行储层的识别。在此基础上进行正演模拟,研究了地震的极限分辨率及不同厚度砂体的地震响应特征,确定了运用叠前地质统计学反演为核心的储层预测技术对该研究区太原组进行储层预测研究,以解决该区储层薄、横向变化快、单一岩石物理参数无法区分岩性等问题。地质统计学反演结果表明,该方法能有效的预测厚度大于3 m的储层。对比研究区内11口测井解释厚度与储层反演厚度表明,储层反演预测厚度平均误差为7.5%,其中5口盲井的平均误差为10.2%,一口新钻井的砂体厚度预测误差为1.73%,为该区的井位部署提供了可靠的资料参考。      

3D geomechanical modeling and estimating the compaction and subsidence of Fahlian reservoir formation (X-field in SW of Iran)

A geomechanical model can reveal the mechanical behavior of rocks and be used to manage the reservoir programs in a better mode. Fluid pressure will be reduced during hydrocarbon production from a reservoir. This reduction of pressure will increase the effective stress due to overburden sediments and will cause porous media compaction and surface subsidence. In some oil fields, the compacting reservoir can support oil and gas production. However, the phenomena can also cause the loss of wells and reduced production and also cause irreparable damage to the surface structures and affect the surrounding environment. For a detailed study of the geomechanical behavior of a hydrocarbon field, a 3D numerical model to describe the reservoir geomechanical characteristics is essential. During this study, using available data and information, a coupled fluid flow-geomechanic model of Fahlian reservoir formation in X-field in SW of Iran was constructed to estimate the amount of land subsidence. According to the prepared model, in this field, the maximum amount of the vertical stress is 110 MPa and the maximum amount of the horizontal stress is 94 MPa. At last, this model is used for the prediction of reservoir compaction and subsidence of the surface. The maximum value of estimated ground subsidence in the study equals to 29 mm. It is considered that according to the obtained values of horizontal and vertical movement in the wall of different wells, those movements are not problematic for casing and well production and also the surrounding environment.     

基于模拟退火粒子群优化算法的裂缝型储层各向异性参数地震反演

发育垂直定向排列裂缝的地下岩石可等效为具有水平对称轴的横向各向同性（horizontal transverse isotropic,HTI）介质。针对HTI介质模型,本文研究了裂缝型储层的各向异性参数地震振幅随方位角变化（amplitude variations with azimuth,AVAZ）的反演方法。首先,在地震AVAZ反演流程中,提出采用模拟退火粒子群优化算法实现裂缝型储层各向异性参数反演。之后,通过理论模型测试,验证了基于模拟退火粒子群优化算法的地震AVAZ反演的有效性。最后,将反演方法应用于四川盆地龙马溪组页岩气储层实际方位地震数据;在反演之前先利用傅里叶级数方法估计裂缝方位并对实际数据进行方位校正,以提供更准确的输入数据;通过计算得到的P波、S波各向异性参数可用于评价裂缝发育程度。反演结果表明,研究区域构造顶部裂缝较发育,与地质基本理论一致,验证了反演方法的合理性。     

Compaction and subsidence issues within the petroleum industry: From wilmington to ekofisk and beyond

Hydrocarbon recovery has led to compaction and subsidence from the North Sea, to Venezuela, and to the western coast of the US. Subsidence at the Wilmington and Ekofisk oil fields are two of the most widely recognized examples due both to the magnitude of subsidence as well as the cost of remediation. However, while lesser known, subsidence is a challenge for a number of reservoirs. In Venezuela, subsidence due to reservoir depletion has led to severe flooding along the coast of Lake Maracaibo. In the Netherlands, subsidence at the large Groningen gas field, though only on the order of tens of centimeters, poses significant challenges since large portions of the Netherlands are below sea level and protected by dikes.Reservoir compaction and surface, or seabed, subsidence has many impacts, challenges, solutions, and even benefits. Seabed subsidence at the Ekofisk field, for example, has had a well known effect by reducing platform airgap and resulting in the jacking of platforms in 1987, the barrier placement in 1989, and the Ekofisk II redevelopment in 1998. Likewise, subsidence has led to significant pipeline concerns due to excess compressional or tensional strain. Reservoir compaction, the cause of subsidence, has led to numerous casing deformations and poses a notable challenge for well completion. However, reservoir compaction also provides significant drive energy and greatly contributes to increased production and reserves.     

Impact of time-lapse seismic data for permeability estimation

We consider the impact of using time-lapse seismic data in addition to production data for permeability estimation in a porous medium with multiphase fluid flows, such as a petroleum reservoir under water-assisted production. Since modeling seismic wave propagation in addition to modeling fluid flows in the reservoir is quite involved, it is assumed that the time-lapse seismic data have already been inverted into fluid saturation differences (pseudoseismic data). Because an inversion process often leads to considerable error growth, we will consider pseudoseismic data with large uncertainties. The impact of pseudoseismic data is assessed through permeability estimation with and without such data and through application of some uncertainty measures for the estimated parameters. A multiscale algorithm is used for the parameter estimations, so that potential differences in attainable permeability resolution will be easily revealed. The numerical examples clearly indicate that the permeability estimation problem is stabilized at a higher level of resolution when pseudoseismic data are applied in addition to production data, even if the pseudoseismic data have large associated uncertainties. Use of the parameter uncertainty measures confirm these results.     

岩石物理建模技术在致密砂岩储层预测中的应用——以鄂尔多斯盆地北部H区块为例

岩石物理建模是叠前反演前重要的基础工作。以致密砂岩储层为目标,剖析了岩石物理建模涉及的主要过程。将测井评价与岩石物理建模视为迭代过程,测井评价提供岩石物理建模的输入数据,岩石物理建模控制测井评价参数的质量。在测井参数具有较高质量的情况下,优选岩石物理建模方法,优化关键参数,较为准确地预测了横波速度等弹性参数,为叠前弹性参数反演提供了可靠的基础数据。利用岩石物理解释模板对叠前反演纵横波速度体进行了解释,提高了致密砂岩气层的识别精度,在鄂尔多斯盆地取得了较好的应用效果。     

A fully implicit and consistent finite element framework for modeling reservoir compaction with large deformation and nonlinear flow model. Part II: verification and numerical example

A fully implicit, fully coupled, and fully consistent finite element framework has been formulated in part I of this work for modeling reservoir compaction through linearizing coupled solid and flow field equations and constructing a local material integrator. In part II of this work, we focus on verification and performance analysis of our numerical formulation and computer implementation using several numerical examples. First, we design a cube problem in triaxial compression to verify our numerical formulation and computer code implementation especially for rock formation in compaction using cap plasticity models. The finite element prediction on stresses is compared with the analytical solution. The second problem we select is a strip footing problem popular in the geotechnical area where the evolution of soil consolidation degrees following the diffusion of pore pressure is the main interest. In this example, we demonstrate a good performance of the proposed numerical formulation on solving different shear and compaction-dominated deformation behaviors by varying the footing length. Importantly, an extremely sharp cap model based on real experimental data for Leda clays, a challenging cap model, is successfully applied in this footing problem. Our focus in this work is to model field reservoirs undergoing serious compaction. A reservoir with complex payzone geometries, multiple horizontal wells, and cap plasticity models with sharp cap surfaces has been successfully solved using our fully implicit formulation. The last example is to model a horizontal wellbore damage problem. Finally, the sensitivity of predicted subsidence to nonlinear flow model, cap hardening parameters, and Lode angles have been systemically investigated and documented in detail, which can provide a constructive guidance on how to successfully model field reservoir compaction problems with cap plasticity models.     

Uncertainty quantification of overpressure buildup through inverse modeling of compaction processes in sedimentary basins

This study illustrates a procedure conducive to a preliminary risk analysis of overpressure development in sedimentary basins characterized by alternating depositional events of sandstone and shale layers. The approach rests on two key elements: (1) forward modeling of fluid flow and compaction, and (2) application of a model-complexity reduction technique based on a generalized polynomial chaos expansion (gPCE). The forward model considers a one-dimensional vertical compaction processes. The gPCE model is then used in an inverse modeling context to obtain efficient model parameter estimation and uncertainty quantification. The methodology is applied to two field settings considered in previous literature works, i.e. the Venture Field (Scotian Shelf, Canada) and the Navarin Basin (Bering Sea, Alaska, USA), relying on available porosity and pressure information for model calibration. It is found that the best result is obtained when porosity and pressure data are considered jointly in the model calibration procedure. Uncertainty propagation from unknown input parameters to model outputs, such as pore pressure vertical distribution, is investigated and quantified. This modeling strategy enables one to quantify the relative importance of key phenomena governing the feedback between sediment compaction and fluid flow processes and driving the buildup of fluid overpressure in stratified sedimentary basins characterized by the presence of low-permeability layers. The results here illustrated (1) allow for diagnosis of the critical role played by the parameters of quantitative formulations linking porosity and permeability in compacted shales and (2) provide an explicit and detailed quantification of the effects of their uncertainty in field settings.     

History matching time-lapse seismic data using the ensemble Kalman filter with multiple data assimilations

The ensemble Kalman filter (EnKF) has become a popular method for history matching production and seismic data in petroleum reservoir models. However, it is known that EnKF may fail to give acceptable data matches especially for highly nonlinear problems. In this paper, we introduce a procedure to improve EnKF data matches based on assimilating the same data multiple times with the covariance matrix of the measurement errors multiplied by the number of data assimilations. We prove the equivalence between single and multiple data assimilations for the linear-Gaussian case and present computational evidence that multiple data assimilations can improve EnKF estimates for the nonlinear case. The proposed procedure was tested by assimilating time-lapse seismic data in two synthetic reservoir problems, and the results show significant improvements compared to the standard EnKF. In addition, we review the inversion schemes used in the EnKF analysis and present a rescaling procedure to avoid loss of information during the truncation of small singular values.     

A modified inverse procedure for calibrating parameters in a land subsidence model and its field application in Shanghai,China

Land-subsidence prediction depends on an appropriate subsidence model and the calibration of its parameter values. A modified inverse procedure is developed and applied to calibrate five parameters in a compacting confined aquifer system using records of field data from vertical extensometers and corresponding hydrographs. The inverse procedure of COMPAC (InvCOMPAC) has been used in the past for calibrating vertical hydraulic conductivity of the aquitards, nonrecoverable and recoverable skeletal specific storages of the aquitards, skeletal specific storage of the aquifers, and initial preconsolidation stress within the aquitards. InvCOMPAC is modified to increase robustness in this study. There are two main differences in the modified InvCOMPAC model (MInvCOMPAC). One is that field data are smoothed before diagram analysis to reduce local oscillation of data and remove abnormal data points. A robust locally weighted regression method is applied to smooth the field data. The other difference is that the Newton-Raphson method, with a variable scale factor, is used to conduct the computer-based inverse adjustment procedure. MInvCOMPAC is then applied to calibrate parameters in a land subsidence model of Shanghai, China. Five parameters of aquifers and aquitards at 15 multiple-extensometer sites are calibrated. Vertical deformation of sedimentary layers can be predicted by the one-dimensional COMPAC model with these calibrated parameters at extensometer sites. These calibrated parameters could also serve as good initial values for parameters of three-dimensional regional land subsidence models of Shanghai.     

Stress and Deformation Analysis of Concrete-Facing Sand–Gravel Dam Based on Inversion Parameters

With the long-term operation of the project, the material parameters of concrete-facing sand–gravel dam will change, which brings great difficulty to the scientific and effective stress and deformation analysis. Combining with the measured displacement data, the finite element analysis model of the concrete-facing sand–gravel dam of Heiquan reservoir was established, and the modulus of elasticity and internal friction angle of the dam body were inverted by the measured displacement of the dam, then the simulation analysis of the filling construction process and the reservoir storage process of dam was carried out, and the stress and deformation values of the dam during the construction period and the impoundment period were calculated. The results showed that the parameters obtained from the inversion are smaller than the original parameters, but there is little difference between them. The displacement calculated by finite element inversion was close to the measured displacement value, the overall displacement and stress distribution of the dam body and panel were in line with the general law, and the calculated displacement and stress values were at the normal level. This study provides a reference for parameter inversion and stress and deformation analysis of concrete slab dam through monitoring data analysis.

     

A Critical Comparison of Three Methods for Time-Lapse Time-Shift Calculation

Time-shift, one of the most popular time-lapse seismic attributes, has been widely used in dynamic reservoir characterization by linking it with pressure and geomechanical changes. Therefore, it is important to select appropriate calculation methods according to different time-lapse seismic data quality and time-shift magnitude. To date, there have been various published works comparing different time-shift calculation methods and discussing their advantages and disadvantages. However, most of these comparisons are based only on synthetic tests or single field applications. As the quality of time-lapse seismic data and time-shift magnitude can vary in different fields, one method may not work consistently well for each case. In this paper, a critical comparison of three different time-shift calculation techniques (Hale’s fast cross-correlation, Rickett’s non-linear inversion, and Whitcombe’s correlated leakage method) is provided. The three methods are applied to a set of synthetic data sets that are designed to account for various seismic noise and time-shift magnitudes. They are also applied to four real time-lapse seismic data sets from three North Sea fields. The calculated time-shift results are compared with the input (in synthetic tests) or the real observations from information such as seabed subsidence and compaction (in field applications). Both qualitative and quantitative comparisons are performed. At the end, each of the time-shift methods is evaluated based on different aspects, and the most appropriate method is suggested for each data scenario. All three time-shift methods are found to successfully measure time-shifts. However, Rickett’s non-linear inversion is the most outstanding method, as it gives smooth time-shifts with relatively good accuracy, and the derived time strains are more stable and interpretable.