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1.
The reproduction of the non-stationary distribution and detailed characteristics of geological bodies is the main difficulty of reservoir modeling. Recently developed multiple-point geostatistics can represent a stationary geological body more effectively than traditional methods. When restricted to a stationary hypothesis, multiple-point geostatistical methods cannot simulate a non-stationary geological body effectively, especially when using non-stationary training images (TIs). According to geologic principles, the non-stationary distribution of geological bodies is controlled by a sedimentary model. Therefore, in this paper, we propose auxiliary variables based on the sedimentary model, namely geological vector information (GVI). GVI can characterize the non-stationary distribution of TIs and simulation domains before sequential simulation, and the precision of data event statistics will be enhanced by the sequential simulation’s data event search area limitations under the guidance of GVI. Consequently, the reproduction of non-stationary geological bodies will be improved. The key features of this method are as follows: (1) obtain TIs and geological vector information for simulated areas restricted by sedimentary models; (2) truncate TIs into a number of sub-TIs using a set of cut-off values such that each sub-TI is stationary and the adjacent sub-TIs have a certain similarity; (3) truncate the simulation domain into a number of sub-regions with the same cut-off values used in TI truncation, so that each sub-region corresponds to a number of sub-TIs; (4) use an improved method to scan the TI or TIs and construct a single search tree to restore replicates of data events located in different sub-TIs; and (5) use an improved conditional probability distribution function to perform sequential simulation. A FORTRAN program is implemented based on the SNESIM. 相似文献
2.
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(英文) 总被引：1，自引：0，他引：1
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。 相似文献
3.
L. Y. Hu Y. Liu C. Scheepens A. W. Shultz R. D. Thompson 《Mathematical Geosciences》2014,46(2):227-240
The multiple-point simulation (MPS) method has been increasingly used to describe the complex geologic features of petroleum reservoirs. The MPS method is based on multiple-point statistics from training images that represent geologic patterns of the reservoir heterogeneity. The traditional MPS algorithm, however, requires the training images to be stationary in space, although the spatial distribution of geologic patterns/features is usually nonstationary. Building geologically realistic but statistically stationary training images is somehow contradictory for reservoir modelers. In recent research on MPS, the concept of a training image has been widely extended. The MPS approach is no longer restricted by the size or the stationarity of training images; a training image can be a small geometrical element or a full-field reservoir model. In this paper, the different types of training images and their corresponding MPS algorithms are first reviewed. Then focus is placed on a case where a reservoir model exists, but needs to be conditioned to well data. The existing model can be built by process-based, object-based, or any other type of reservoir modeling approach. In general, the geologic patterns in a reservoir model are constrained by depositional environment, seismic data, or other trend maps. Thus, they are nonstationary, in the sense that they are location dependent. A new MPS algorithm is proposed that can use any existing model as training image and condition it to well data. In particular, this algorithm is a practical solution for conditioning geologic-process-based reservoir models to well data. 相似文献
4.
Conditional Simulation of Complex Geological Structures Using Multiple-Point Statistics 总被引：68，自引：0，他引：68
Sebastien Strebelle 《Mathematical Geology》2002,34(1):1-21
In many earth sciences applications, the geological objects or structures to be reproduced are curvilinear, e.g., sand channels in a clastic reservoir. Their modeling requires multiple-point statistics involving jointly three or more points at a time, much beyond the traditional two-point variogram statistics. Actual data from the field being modeled, particularly if it is subsurface, are rarely enough to allow inference of such multiple-point statistics. The approach proposed in this paper consists of borrowing the required multiple-point statistics from training images depicting the expected patterns of geological heterogeneities. Several training images can be used, reflecting different scales of variability and styles of heterogeneities. The multiple-point statistics inferred from these training image(s) are exported to the geostatistical numerical model where they are anchored to the actual data, both hard and soft, in a sequential simulation mode. The algorithm and code developed are tested for the simulation of a fluvial hydrocarbon reservoir with meandering channels. The methodology proposed appears to be simple (multiple-point statistics are scanned directly from training images), general (any type of random geometry can be considered), and fast enough to handle large 3D simulation grids. 相似文献
5.
Application of multiple-point geostatistics on modelling groundwater flow and transport in a cross-bedded aquifer (Belgium) 总被引：3，自引：1，他引：2
Sedimentological processes often result in complex three-dimensional subsurface heterogeneity of hydrogeological parameter values. Variogram-based stochastic approaches are often not able to describe heterogeneity in such complex geological environments. This work shows how multiple-point geostatistics can be applied in a realistic hydrogeological application to determine the impact of complex geological heterogeneity on groundwater flow and transport. The approach is applied to a real aquifer in Belgium that exhibits a complex sedimentary heterogeneity and anisotropy. A training image is constructed based on geological and hydrogeological field data. Multiple-point statistics are borrowed from this training image to simulate hydrofacies occurrence, while intrafacies permeability variability is simulated using conventional variogram-based geostatistical methods. The simulated hydraulic conductivity realizations are used as input to a groundwater flow and transport model to investigate the effect of small-scale sedimentary heterogeneity on contaminant plume migration. Results show that small-scale sedimentary heterogeneity has a significant effect on contaminant transport in the studied aquifer. The uncertainty on the spatial facies distribution and intrafacies hydraulic conductivity distribution results in a significant uncertainty on the calculated concentration distribution. Comparison with standard variogram-based techniques shows that multiple-point geostatistics allow better reproduction of irregularly shaped low-permeability clay drapes that influence solute transport. 相似文献
6.
The advent of multiple-point geostatistics (MPS) gave rise to the integration of complex subsurface geological structures
and features into the model by the concept of training images. Initial algorithms generate geologically realistic realizations
by using these training images to obtain conditional probabilities needed in a stochastic simulation framework. More recent
pattern-based geostatistical algorithms attempt to improve the accuracy of the training image pattern reproduction. In these
approaches, the training image is used to construct a pattern database. Consequently, sequential simulation will be carried
out by selecting a pattern from the database and pasting it onto the simulation grid. One of the shortcomings of the present
algorithms is the lack of a unifying framework for classifying and modeling the patterns from the training image. In this
paper, an entirely different approach will be taken toward geostatistical modeling. A novel, principled and unified technique
for pattern analysis and generation that ensures computational efficiency and enables a straightforward incorporation of domain
knowledge will be presented. 相似文献
7.
8.
Validation Techniques for Geological Patterns Simulations Based on Variogram and Multiple-Point Statistics 总被引：2，自引：2，他引：0
Traditional simulation methods that are based on some form of kriging are not sensitive to the presence of strings of connectivity
of low or high values. They are particularly inappropriate in many earth sciences applications, where the geological structures
to be simulated are curvilinear. In such cases, techniques allowing the reproduction of multiple-point statistics are required.
The aim of this paper is to point out the advantages of integrating such multiple-statistics in a model in order to allow
shape reproduction, as well as heterogeneity structures, of complex geological patterns to emerge. A comparison between a
traditional variogram-based simulation algorithm, such as the sequential indicator simulation, and a multiple-point statistics
algorithm (e.g., the single normal equation simulation) is presented. In particular, it is shown that the spatial distribution
of limestone with meandering channels in Lecce, Italy is better reproduced by using the latter algorithm. The strengths of
this study are, first, the use of a training image that is not a fluvial system and, more importantly, the quantitative comparison
between the two algorithms. The paper focuses on different metrics that facilitate the comparison of the methods used for
limestone spatial distribution simulation: both objective measures of similarity of facies realizations and high-order spatial
cumulants based on different third- and fourth-order spatial templates are considered. 相似文献
9.
Fast FILTERSIM Simulation with Score-based Distance 总被引：5，自引：3，他引：2
FILTERSIM is a pattern-based multiple-point geostatistical algorithm for modeling both continuous and categorical variables.
It first groups all the patterns from a training image into a set of pattern classes using their filter scores. At each simulation
location, FILTERSIM identifies the training pattern class closest to the local conditioning data event, then samples a training
pattern from that prototype class and pastes it onto the simulation grid. In the original FILTERSIM algorithm, the selection
of the closest pattern class is based on the pixel-wise distance between the prototype of each training pattern class and
the local conditioning data event. Hence, FILTERSIM is computationally intensive for 3D simulations, especially with a large
and pattern-rich training image. In this paper, a novel approach is proposed to accelerate the simulation process by replacing
that pixel-wise distance calculation with a filter score comparison, which is the difference between the filter score of local
conditioning data event and that of each pattern prototype. This score-based distance calculation significantly reduces the
CPU consumption due to the tremendous data dimension reduction. The results show that this new score based-distance calculation
can speed up FILTERSIM simulation by a factor up to 10 in 3D applications. 相似文献
10.
Luis Manuel de Vries Jesus Carrera Oriol Falivene Oscar Gratacós Luit Jan Slooten 《Mathematical Geosciences》2009,41(1):29-42
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. 相似文献
11.
Spatially distributed and varying natural phenomena encountered in geoscience and engineering problem solving are typically
incompatible with Gaussian models, exhibiting nonlinear spatial patterns and complex, multiple-point connectivity of extreme
values. Stochastic simulation of such phenomena is historically founded on second-order spatial statistical approaches, which
are limited in their capacity to model complex spatial uncertainty. The newer multiple-point (MP) simulation framework addresses
past limits by establishing the concept of a training image, and, arguably, has its own drawbacks. An alternative to current
MP approaches is founded upon new high-order measures of spatial complexity, termed “high-order spatial cumulants.” These
are combinations of moments of statistical parameters that characterize non-Gaussian random fields and can describe complex
spatial information. Stochastic simulation of complex spatial processes is developed based on high-order spatial cumulants
in the high-dimensional space of Legendre polynomials. Starting with discrete Legendre polynomials, a set of discrete orthogonal
cumulants is introduced as a tool to characterize spatial shapes. Weighted orthonormal Legendre polynomials define the so-called
Legendre cumulants that are high-order conditional spatial cumulants inferred from training images and are combined with available
sparse data sets. Advantages of the high-order sequential simulation approach developed herein include the absence of any
distribution-related assumptions and pre- or post-processing steps. The method is shown to generate realizations of complex
spatial patterns, reproduce bimodal data distributions, data variograms, and high-order spatial cumulants of the data. In
addition, it is shown that the available hard data dominate the simulation process and have a definitive effect on the simulated
realizations, whereas the training images are only used to fill in high-order relations that cannot be inferred from data.
Compared to the MP framework, the proposed approach is data-driven and consistently reconstructs the lower-order spatial complexity
in the data used, in addition to high order. 相似文献
12.
Xiulan He Torben O. Sonnenborg Flemming Jørgensen Karsten H. Jensen 《Hydrogeology Journal》2017,25(2):359-370
Stationarity has traditionally been a requirement of geostatistical simulations. A common way to deal with non-stationarity is to divide the system into stationary sub-regions and subsequently merge the realizations for each region. Recently, the so-called partition approach that has the flexibility to model non-stationary systems directly was developed for multiple-point statistics simulation (MPS). The objective of this study is to apply the MPS partition method with conventional borehole logs and high-resolution airborne electromagnetic (AEM) data, for simulation of a real-world non-stationary geological system characterized by a network of connected buried valleys that incise deeply into layered Miocene sediments (case study in Denmark). The results show that, based on fragmented information of the formation boundaries, the MPS partition method is able to simulate a non-stationary system including valley structures embedded in a layered Miocene sequence in a single run. Besides, statistical information retrieved from the AEM data improved the simulation of the geology significantly, especially for the deep-seated buried valley sediments where borehole information is sparse. 相似文献
13.
多点地质统计学建模的发展趋势 总被引：2，自引：0，他引：2
从算法研究、训练图像处理和实际应用三个方面详细解剖了国内外多点地质统计学的发展历程,在此基础上,分析了多点地质统计学主流的几种算法的核心原理、适用范围及优缺点,以此来对储层建模的发展趋势作出展望。目前,多点地质统计学虽是随机建模的一种前沿研究热点,但由于其尚未成熟,仍需对建模算法进行研究。为此,在前人研究的基础上,重点分析了多点地质统计学的发展趋势：合理处理训练图像;合理利用软信息;选择合适的相似性方法;选择合适的标准化方法;合理利用平稳性;算法间的耦合;选择合适的过滤器;拓展缝洞型碳酸盐岩模拟。最后,提出多点地质统计学在储层建模方面,应从增加储层的模拟区域、提高模拟精度、扩大储层相的模拟范围和提高计算机模拟效率等方面进行改进。 相似文献
14.
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. 相似文献
15.
Direct Multiple-Point Geostatistical Simulation of Edge Properties for Modeling Thin Irregularly Shaped Surfaces 总被引：3，自引：1，他引：2
Thin, irregularly shaped surfaces such as clay drapes often have a major control on flow and transport in heterogeneous porous
media. Clay drapes are often complex, curvilinear three-dimensional surfaces and display a very complex spatial distribution.
Variogram-based stochastic approaches are also often not able to describe the spatial distribution of clay drapes since complex,
curvilinear, continuous, and interconnected structures cannot be characterized using only two-point statistics. Multiple-point
geostatistics aims to overcome the limitations of the variogram. The premise of multiple-point geostatistics is to move beyond
two-point correlations between variables and to obtain (cross) correlation moments at three or more locations at a time using
training images to characterize the patterns of geological heterogeneity. Multiple-point geostatistics can reproduce thin
irregularly shaped surfaces such as clay drapes, but this is often computationally very intensive. This paper describes and
applies a methodology to simulate thin, irregularly shaped surfaces with a smaller CPU and RAM demand than the conventional
multiple-point statistical methods. The proposed method uses edge properties for indicating the presence of thin irregularly
shaped surfaces. Instead of pixel values, edge properties indicating the presence of irregularly shaped surfaces are simulated
using snesim. This method allows direct simulation of edge properties instead of pixel properties to make it possible to perform multiple-point
geostatistical simulations with a larger cell size and thus a smaller computation time and memory demand. This method is particularly
valuable for three-dimensional applications of multiple-point geostatistics. 相似文献
16.
Geostatistical Seismic Inversion with Direct Sequential Simulation and Co-simulation with Multi-local Distribution Functions 总被引：1，自引：0，他引：1
Rúben Nunes Amílcar Soares Leonardo Azevedo Pedro Pereira 《Mathematical Geosciences》2017,49(5):583-601
Stochastic sequential simulation is a common modelling technique used in Earth sciences and an integral part of iterative geostatistical seismic inversion methodologies. Traditional stochastic sequential simulation techniques based on bi-point statistics assume, for the entire study area, stationarity of the spatial continuity pattern and a single probability distribution function, as revealed by a single variogram model and inferred from the available experimental data, respectively. In this paper, the traditional direct sequential simulation algorithm is extended to handle non-stationary natural phenomena. The proposed stochastic sequential simulation algorithm can take into consideration multiple regionalized spatial continuity patterns and probability distribution functions, depending on the spatial location of the grid node to be simulated. This work shows the application and discusses the benefits of the proposed stochastic sequential simulation as part of an iterative geostatistical seismic inversion methodology in two distinct geological environments in which non-stationarity behaviour can be assessed by the simultaneous interpretation of the available well-log and seismic reflection data. The results show that the elastic models generated by the proposed stochastic sequential simulation are able to reproduce simultaneously the regional and global variogram models and target distribution functions relative to the average volume of each sub-region. When used as part of a geostatistical seismic inversion procedure, the retrieved inverse models are more geologically realistic, since they incorporate the knowledge of the subsurface geology as provided, for example, by seismic and well-log data interpretation. 相似文献
17.
High-order Statistics of Spatial Random Fields: Exploring Spatial Cumulants for Modeling Complex Non-Gaussian and Non-linear Phenomena 总被引：9，自引：7，他引：2
The spatial distributions of earth science and engineering phenomena under study are currently predicted from finite measurements
and second-order geostatistical models. The latter models can be limiting, as geological systems are highly complex, non-Gaussian,
and exhibit non-linear patterns of spatial connectivity. Non-linear and non-Gaussian high-order geostatistics based on spatial
connectivity measures, namely spatial cumulants, are proposed as a new alternative modeling framework for spatial data. This
framework has two parts. The first part is the definition, properties, and inference of spatial cumulants—including understanding
the interrelation of cumulant characteristics with the in-situ behavior of geological entities or processes, as examined in
this paper. The second part is the research on a random field model for simulation based on its high-order spatial cumulants.
Mathematical definitions of non-Gaussian spatial random functions and their high-order spatial statistics are presented herein,
stressing the notion of spatial cumulants. The calculation of spatial cumulants with spatial templates follows, including
anisotropic experimental cumulants. Several examples of two- and three-dimensional images, including a diamond bearing kimberlite
pipe from the Ekati Mine in Canada, are analyzed to assess the relations between cumulants and the spatial behavior of geological
processes. Spatial cumulants of orders three to five are shown to capture directional multiple-point periodicity, connectivity
including connectivity of extreme values, and spatial architecture. In addition, they provide substantial information on geometric
characteristics and anisotropy of geological patterns. It is further shown that effects of complex spatial patterns are seen
even if only subsets of all cumulant templates are computed. Compared to second-order statistics, cumulant maps are found
to include a wealth of additional information from underlying geological patterns. Further work seeks to integrate this information
in the predictive capabilities of a random field model. 相似文献
18.
Solving Speed and Memory Issues in Multiple-Point Statistics Simulation Program SNESIM 总被引：2，自引：2，他引：0
In the last 10 years, Multiple-Point Statistics (MPS) modeling has emerged in Geostatistics as a valuable alternative to traditional variogram-based and object-based modeling. In contrast to variogram-based simulation, which is limited to two-point correlation reproduction, MPS simulation extracts and reproduces multiple-point statistics moments from training images; this allows modeling geologically realistic features, such as channels that control reservoir connectivity and flow behavior. In addition, MPS simulation works on individual pixels or small groups of pixels (patterns), thus does not suffer from the same data conditioning limitations as object-based simulation. The Single Normal Equation Simulation program SNESIM was the first implementation of MPS simulation to propose, through the introduction of search trees, an efficient solution to the extraction and storage of multiple-point statistics moments from training images. SNESIM is able to simulate three-dimensional models; however, memory and speed issues can occur when applying it to multimillion cell grids. Several other implementations of MPS simulation were proposed after SNESIM, but most of them manage to reduce memory demand or simulation time only at the expense of data conditioning exactitude and/or training pattern reproduction quality. In this paper, the original SNESIM program is revisited, and solutions are presented to eliminate both memory demand and simulation time limitations. First, we demonstrate that the time needed to simulate a grid node is a direct function of the number of uninformed locations in the conditioning data search neighborhood. Thus, two improvements are proposed to maximize the ratio of informed to uniformed locations in search neighborhoods: a new multiple-grid approach introducing additional intermediary subgrids; and a new search neighborhood designing process to preferentially include previously simulated node locations. Finally, because SNESIM memory demand and simulation time increase with the size of the data template used to extract multiple-point statistics moments from the training image and build the search tree, a simple method is described to minimize data template sizes while preserving training pattern reproduction quality. 相似文献
19.
The resolution of measurement devices can be insufficient for certain purposes. We propose to stochastically simulate spatial
features at scales smaller than the measurement resolution. This is accomplished using multiple-point geostatistical simulation
(direct sampling in the present case) to interpolate values at the target scale. These structures are inferred using hypothesis
of scale invariance and stationarity on the spatial patterns found at the coarse scale. The proposed multiple-point super-resolution
mapping method is able to deal with “both continuous and categorical variables,” and can be extended to multivariate problems.
The advantages and limitations of the approach are illustrated with examples from satellite imaging. 相似文献
20.
利用三维地质模拟技术重构地质现象的三维空间分布,是实现自然资源管理和风险评估的重要基础和前提。多点统计学方法通过探寻多点间的空间结构关系,结合随机模拟方法生成具有差异性的模拟结果,较好地再现了复杂的地质现象。然而,如何构建合适、有效的训练图像一直是基于多点统计学三维地质模拟的核心问题。本文提出了一种改进的多点统计学算法。本方法结合了序贯模拟和迭代的方法,将二维剖面扩展为三维训练图像,再结合EM-Like算法,实现了三维地质结构的优化模拟。建模实例结果表明,本方法能确保训练图像对内部模拟网格的约束,准确模拟研究区的地层层序,并很好地再现二维地质剖面所反映的地层结构关系。 相似文献