Multiple-Point Simulations Constrained by Continuous Auxiliary Data

An important issue of using the multiple-point (MP) statistical approach for reservoir modeling concerns the integration of auxiliary constraints derived, for instance, from seismic information. There exist two methods in the literature for these non-stationary MP simulations. One is based on an analytical approximation (the “τ-model”) of the conditional probabilities that involve auxiliary data. The degree of approximation with this method depends on the parameter τ, whose inference is difficult in practice. The other method is based on the inference of these conditional probabilities directly from training images. This method classifies the auxiliary data into a few classes. This classification is in general arbitrary and therefore inconvenient in practice, especially in the case of continuous auxiliary constraints. In this paper, we propose an alternative method for performing non-stationary MP simulations. This method accounts for the data support in the modeling procedure and allows, in particular, continuous auxiliary data to be integrated into MP simulations. This method avoids the major limitations of the previous methods, namely the use of an approximate analytical model and the reduction of the auxiliary data into a limited number of classes. This method can be easily implemented in the existing MP simulation codes. Numerical tests show good performance of this method both in reproducing the geometrical features of the training image and in honouring the auxiliary data.     

储层地质建模的现状与展望

储层地质建模对于科学的油藏评价、油藏开发管理以及三维油藏数值模拟具有很大的意义。目前已有的建模算法和商业软件可满足地质特征三维分布的图形要求,并可进行初步的井间预测,但预测精度有待于进一步提高。简要介绍了各种建模方法研究现状,分析了已有算法中亟需改进的问题,并从建模算法的改进、原型模型的丰富、地震信息的整合以及加强地质约束等方面论述了储层地质建模的发展前景。     

Application of Multiple Point Geostatistics to Non-stationary Images

Simulation of flow and solute transport through aquifers or oil reservoirs requires a precise representation of subsurface heterogeneity that can be achieved by stochastic simulation approaches. Traditional geostatistical methods based on variograms, such as truncated Gaussian simulation or sequential indicator simulation, may fail to generate the complex, curvilinear, continuous and interconnected facies distributions that are often encountered in real geological media, due to their reliance on two-point statistics. Multiple Point Geostatistics (MPG) overcomes this constraint by using more complex point configurations whose statistics are retrieved from training images. Obtaining representative statistics requires stationary training images, but geological understanding often suggests a priori facies variability patterns. This research aims at extending MPG to non-stationary facies distributions. The proposed method subdivides the training images into different areas. The statistics for each area are stored in separate frequency search trees. Several training images are used to ensure that the obtained statistics are representative. The facies probability distribution for each cell during simulation is calculated by weighting the probabilities from the frequency trees. The method is tested on two different object-based training image sets. Results show that non-stationary training images can be used to generate suitable non-stationary facies distributions.     

Simulation of mineral grades with hard and soft conditioning data: application to a porphyry copper deposit

This work deals with the geostatistical simulation of mineral grades whose distribution exhibits spatial trends within the ore deposit. It is suggested that these trends can be reproduced by using a stationary random field model and by conditioning the realizations to data that incorporate the available information on the local grade distribution. These can be hard data (e.g., assays on samples) or soft data (e.g., rock-type information) that account for expert geological knowledge and supply the lack of hard data in scarcely sampled areas. Two algorithms are proposed, depending on the kind of soft data under consideration: interval constraints or local moment constraints. An application to a porphyry copper deposit is presented, in which it is shown that the incorporation of soft conditioning data associated with the prevailing rock type improves the modeling of the uncertainty in the actual copper grades.     

A Blocking Markov Chain Monte Carlo Method for Inverse Stochastic Hydrogeological Modeling

An adequate representation of the detailed spatial variation of subsurface parameters for underground flow and mass transport simulation entails heterogeneous models. Uncertainty characterization generally calls for a Monte Carlo analysis of many equally likely realizations that honor both direct information (e.g., conductivity data) and information about the state of the system (e.g., piezometric head or concentration data). Thus, the problems faced is how to generate multiple realizations conditioned to parameter data, and inverse-conditioned to dependent state data. We propose using Markov chain Monte Carlo approach (MCMC) with block updating and combined with upscaling to achieve this purpose. Our proposal presents an alternative block updating scheme that permits the application of MCMC to inverse stochastic simulation of heterogeneous fields and incorporates upscaling in a multi-grid approach to speed up the generation of the realizations. The main advantage of MCMC, compared to other methods capable of generating inverse-conditioned realizations (such as the self-calibrating or the pilot point methods), is that it does not require the solution of a complex optimization inverse problem, although it requires the solution of the direct problem many times.     

Two Artifacts of Probability Field Simulation

Probability field simulation is being used increasingly to simulate geostatistical realizations. The method can be faster than conventional simulation algorithms and it is well suited to integrate prior soft information in the form of local probability distributions. The theoretical basis of probability field simulation has been established when there are no conditioning data; however, no such basis has been established in presence of conditioning data. Realizations generated by probability field simulation show two severe artifacts near conditioning data. We document these artifacts and show theoretically why they exist. The two artifacts that have been investigated are (1) local conditioning data appear as local minima or maxima of the simulated values, and (2) the variogram model in range of conditioning data is not honored; the simulated values have significantly greater continuity than they are supposed to. These two artifacts are predicted by theory. An example flow simulation study is presented to illustrate that they affect more than the visual appearance of the simulated realizations. Notwithstanding the flexibility of the probability field simulation method, these two artifacts suggest that it be used with caution in presence of conditioning data. Future research may overcome these limitations.     

Evaluating and classifying contaminated areas based on loss functions using annealing simulations

This paper presents a methodology based on geostatistical theory for quantifying the risks associated with heavy-metal contamination in the harbor area of Santana, Amapá State, Northern Brazil. In this area there were activities related to the commercialization of manganese ore from Serra do Navio. Manganese and arsenic concentrations at unsampled sites were estimated by postprocessing results from stochastic annealing simulations; the simulations were used to test different criteria for optimization, including average, median, and quantiles. For classifying areas as contaminated or uncontaminated, estimated quantiles based on functions of asymmetric loss showed better results than did estimates based on symmetric loss, such as the average or the median. The use of specific loss functions in the decision-making process can reduce the costs of remediation and health maintenance. The highest global health costs were observed for manganese.     

Simulation of Stratigraphic Architecture from Statistical and Geometrical Characterizations

Stratigraphic modeling based on physical and geologic principles has been improved by more sophisticated process models and increased computer power. However, such efforts may reach a limit in their predictive power because of the stochastic, multiscaled nature of the physical processes involved. Building on techniques from the geostatistical literature, a conditional simulation method, dubbed SimStrat, has been developed to improve predictions of stratigraphic architecture from limited data. No physical processes are invoked. Rather, the prediction is based solely on geometric and statistical principals. The method takes as input sonar bathymetry, seismically defined stratigraphic horizons, and core-defined horizons. Each stratigraphic horizon is characterized using spectral modeling and coherence modeling for adjacent horizons. Predictions of subsurface horizons are improved where seafloor bathymetry conforms with the underlying strata. Conditional simulations can then be generated that conform to available data constraints and statistical characterization. Tests with synthetic data in one and two dimensions for differing spectral models confirm the reliability of the method.     

三维多极距中梯测深的模拟研究

多极距中梯测深法是一种效率高、信息丰富的新型体积测深技术,而当前常规多极距中梯测深应用与研究多数局限于二维空间,其三维正反演一直是人们研究的热点。本文在四面体交错网格剖分基础上,采用有限单元法对球体等三维模型进行多极距中梯测深数值模拟计算。研究表明,三维数值模拟可有效反映模型的空间分布;在不增加太多工作量的情况下,实现高效体积测深;电阻率和极化率参数模拟相结合分析,模拟精度高,稳定性好;开展倾斜铜板、铜块水槽物理模拟,模拟结果较好反映了模型的空间及电性分布,验证了多极距中梯测深的可行性和正确性,为该方法的实际应用及后续的反演工作提供了重要依据。     

Visualising data distributions with kernel density estimation and reduced chi-squared statistic

The application of frequency distribution statistics to data provides objective means to assess the nature of the data distribution and viability of numerical models that are used to visualize and interpret data. Two commonly used tools are the kernel density estimation and reduced chi-squared statistic used in combination with a weighted mean. Due to the wide applicability of these tools, we present a Java-based computer application called KDX to facilitate the visualization of data and the utilization of these numerical tools.     

多尺度随机孔洞介质地震波正演及其逆时成像

常规地震勘探理论无法完全解释复杂多变的地质特征,较难达到高精度地震资料处理的目的,因此必须发展适应复杂非均匀介质的地震波场传播理论,以更好地刻画真实的复杂构造、岩性、裂隙油气藏的特点。根据实际火山岩样的随机特征,构建了相应的多尺度组合型随机孔洞介质模型,并进行了高精度地震波正演数值模拟和逆时成像研究,制作了在不同频率条件下的自激自收剖面和逆时偏移剖面,计算结果表明,构建的多尺度随机孔洞介质模型可以有效模拟真实的地质变化特征,同时指出准确区分由地层随机非均匀性引起的散射波场响应和干扰信号是实现高分辨率地震勘探的前提。     

江苏瓦庄油田油藏数值模拟开发技术政策界限研究

针对江苏瓦庄油田窄条状、长井段、多油层、薄互层、多断层的特点,采用地质建模和油藏数值模拟一体化的技术思路,在构造研究、精细地层对比、沉积相分析和测井分析的基础上,建立了三维油藏地质模型,以该模型为静态地质模型进行精细油藏数值模拟研究,在历史拟合成功的基础上,进行了开发层系、油井距断层距离、分层配注的开发技术政策界限研究,得出了该类油田合理的开发政策,为油田的开发生产提供了合理的理论指导。     

东亚地区区域气候模拟的研究进展

由于大气环流模式对东亚地区区域气候特征的模拟存在很大不足,采用区域气候模式模拟该地区特殊的季风气候成为目前发展的一个重要研究方向,并取得了显著的研究进展。通过回顾当前东亚地区区域气候模拟的现状,表明大部分区域气候模式都不同程度地模拟出了东亚季风区持续性洪涝现象的大尺度环流特征和演变过程,再现了东亚各主要气候区降水的年际、季节和季节内变化及主要雨带的季节进退和降水的时空演变特征。但是,大部分模式没能很好地模拟出大尺度特征的强度和量值,模拟的温度和降水存在系统性偏差。原因分析表明,进一步完善和改进区域气候模式的物理过程参数化方案及动力框架可以改善模拟效果。最后对区域气候模式未来的发展给出展望。     

基于三维渗流模拟的坝基渗漏和渗透稳定分析——以哇沿水库为例

水库坝基渗漏不但损失水库蓄水量,更重要的会引起大坝渗透变形失去稳定。应用三维地下水流数值模拟计算坝基渗漏量和分析渗透稳定,较好地解决了周边与底面边界的不规则问题和垂向上地层的非均质问题,提高了计算精度。以青海省哇沿水库为例,在充分分析水库坝基水文地质条件的基础上,建立了坝基渗漏三维地下水流数值模型,模拟了设置不同深度防渗墙时的渗漏量和坝后出溢段水力坡度。评价了大坝的渗透稳定性,为防止哇沿水库发生渗透变形,设置防渗墙深度应大于50m。当防渗墙深度为50m时,水库渗漏量为12 012m~3/d。     

在储层建模中利用多点地质统计学整合地质概念模型及其解释

基于三维空间中稀疏的观测数据,地质学家和储层建模人员尝试预测井间的地质沉积相的空间非均质性时,地质概念模型和先验认识在其中扮演着重要的角色。这种整合先验模型或解释的过程有时是隐蔽或不易察觉的,正如在手工绘等值线图中的情形;它也能够被显式地运用到某种算法当中,比如数字绘图中的算法。新近兴起的多点地质统计学为地质学家和储层建模人员提供了一种有力工具,它强调使用训练图像把先验模型明确而定量地引入到储层建模当中。先验地质模型包含了被研究的真实储层中确信存在的样式,而训练图像则是该模型的定量化表达。通过再现高阶统计量,多点算法能够从训练图像中捕捉复杂的(非线性)特征样式并把它们锚定到观测的井位数据。文中描述了多点地质统计学原理,以突出训练图像概念重要性为主线,描述了多点地质统计学在建立三维储层模型中的应用。     

封堵评价用微裂缝岩心的模拟及模拟封堵实验

采用不同厚度的金属箔片和胶凝材料浇筑出了微裂缝岩心,配合高温高压失水仪外筒和泥浆杯,通过监测30 min内的漏失量,即可开展微裂缝岩心封堵评价实验,评价钻井液的封堵效果。通过微观观察法和流量计算法对制作的微裂缝的表面形态和开度进行了验证,结果表明岩心缝面具有一定的粗糙度,裂缝开度符合实验设计,最小3.33 μm,且岩心具有5～10 cm的裂缝行程。微裂缝岩心制作方法简单,重复率高,通过室内实验验证了制作的微裂缝岩心可以用于钻井液封堵材料的封堵性能评价,为微裂缝封堵评价实验提供了岩心模块,弥补了使用缝板模拟裂缝表面光滑和采用砂床钢珠砂盘等孔隙介质换算裂缝开度的不足。     

电缆地层测试器的有限元数值模拟

电缆地层测试器的数值模拟是仪器研制和测井解释方法研究的基础。应用有限元技术,建立了三维电缆地层测试器的数值模拟程序。在理论研究方面,提出了可变管线存储体积的边界条件。在程序研究方面,采用时间的向后差分解决了程序的稳定性问题;采用时间的变步长技术提高了程序的运行效率。     

偏心跟管钻具钻进的仿真分析

针对偏心跟管钻具工作环境与受力作用复杂的情况,通过建立跟管钻具在地层中钻进的有限元模型,设定各种边界条件及载荷,运用有限元分析软件ANSYS 12.0对跟管钻具的钻进工况进行仿真模拟,分析钻具在钻进时与地层岩土体相互作用下的应力应变情况。根据模拟分析结果能够更清楚地了解钻具钻进时的应力状态,并对钻具的设计、优化起到指导性作用以及为钻具设计结构的合理性提供了理论依据。     

考虑气压势影响的降雨入渗数值模拟研究

利用一维下渗模型的数值模拟方法研究下渗试验过程中气压势与饱和水力传导度K_s的关系。数值分析表明,可通过由下渗过程中表层湿润的饱和度来折减K_s值的途径考虑气压势的影响,从而改进计算方法。下渗试验的模拟计算结果表明,改进后的方法比常用的方法有更高的精度。     

Multiscale finite-volume formulation for multiphase flow in porous media: black oil formulation of compressible,three-phase flow with gravity

Most practical reservoir simulation studies are performed using the so-called black oil model, in which the phase behavior is represented using solubilities and formation volume factors. We extend the multiscale finite-volume (MSFV) method to deal with nonlinear immiscible three-phase compressible flow in the presence of gravity and capillary forces (i.e., black oil model). Consistent with the MSFV framework, flow and transport are treated separately and differently using a sequential implicit algorithm. A multiscale operator splitting strategy is used to solve the overall mass balance (i.e., the pressure equation). The black-oil pressure equation, which is nonlinear and parabolic, is decomposed into three parts. The first is a homo geneous elliptic equation, for which the original MSFV method is used to compute the dual basis functions and the coarse-scale transmissibilities. The second equation accounts for gravity and capillary effects; the third equation accounts for mass accumulation and sources/ sinks (wells). With the basis functions of the elliptic part, the coarse-scale operator can be assembled. The gravity/capillary pressure part is made up of an elliptic part and a correction term, which is computed using solutions of gravity-driven local problems. A particular solution represents accumulation and wells. The reconstructed fine-scale pressure is used to compute the fine-scale phase fluxes, which are then used to solve the nonlinear saturation equations. For this purpose, a Schwarz iterative scheme is used on the primal coarse grid. The framework is demonstrated using challenging black-oil examples of nonlinear compressible multiphase flow in strongly heterogeneous formations.