A three-dimensional high-resolution reservoir model of the Eocene Shahejie Formation in Bohai Bay Basin,integrating stratigraphic forward modeling and geostatistics

Reservoir characterization based on geostatistics method requires well constraints (e.g. seismic data with high quality) to predict inter-well reservoir quality that is conformed to geological laws. Nevertheless, the resolution of seismic data in multiple basins or reservoirs is not high enough to recognize the distribution of different types of sand bodies. In this paper, we propose a new method to improve the precision of reservoir characterization: reservoir modeling with the constrains of sedimentary process model and sedimentary microfacies. We employed stratigraphic forward modeling, a process-based method, to constrain the reservoir modeling in one oil-bearing interval of the third member of Eocene Shahejie Formation in J-Oilfield of Liaoxi Sag, Bohai Bay Basin.We divide reservoir modeling into two orders using different types of constrains. In the first order, we use the simulated shale model from stratigraphic forward model that is corrected by wells data as a 3D trend volume to constrain the reservoir sand-shale modeling. In the second order, different types of sedimentary microfacies in the sandy part of the model are further recognized and simulated within the constrains of sedimentary microfacies maps. Consequently, the porosity, permeability and oil saturation are modeled under the control of precise sedimentary microfacies model. The high-resolution reservoir model shows that the porosity, permeability and oil saturation of distributary channel is generally above 20%, 10md and 50%, respectively, which are much higher than that of other types of sedimentary microfacies. It can be concluded that comparing to other types of sedimentary facies, distributary channel has better physical properties and more oil accumulation in the fan-delta front and therefore is the most favorable zones for petroleum development in the research area.     

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.     

Representing Spatial Uncertainty Using Distances and Kernels

Assessing uncertainty of a spatial phenomenon requires the analysis of a large number of parameters which must be processed by a transfer function. To capture the possibly of a wide range of uncertainty in the transfer function response, a large set of geostatistical model realizations needs to be processed. Stochastic spatial simulation can rapidly provide multiple, equally probable realizations. However, since the transfer function is often computationally demanding, only a small number of models can be evaluated in practice, and are usually selected through a ranking procedure. Traditional ranking techniques for selection of probabilistic ranges of response (P10, P50 and P90) are highly dependent on the static property used. In this paper, we propose to parameterize the spatial uncertainty represented by a large set of geostatistical realizations through a distance function measuring “dissimilarity” between any two geostatistical realizations. The distance function allows a mapping of the space of uncertainty. The distance can be tailored to the particular problem. The multi-dimensional space of uncertainty can be modeled using kernel techniques, such as kernel principal component analysis (KPCA) or kernel clustering. These tools allow for the selection of a subset of representative realizations containing similar properties to the larger set. Without losing accuracy, decisions and strategies can then be performed applying a transfer function on the subset without the need to exhaustively evaluate each realization. This method is applied to a synthetic oil reservoir, where spatial uncertainty of channel facies is modeled through multiple realizations generated using a multi-point geostatistical algorithm and several training images.     

Kriging in the Presence of Locally Varying Anisotropy Using Non-Euclidean Distances

A stationary specification of anisotropy does not always capture the complexities of a geologic site. In this situation, the anisotropy can be varied locally. Directions of continuity and the range of the variogram can change depending on location within the domain being modeled. Kriging equations have been developed to use a local anisotropy specification within kriging neighborhoods; however, this approach does not account for variation in anisotropy within the kriging neighborhood. This paper presents an algorithm to determine the optimum path between points that results in the highest covariance in the presence of locally varying anisotropy. Using optimum paths increases covariance, results in lower estimation variance and leads to results that reflect important curvilinear structures. Although CPU intensive, the complex curvilinear structures of the kriged maps are important for process evaluation. Examples highlight the ability of this methodology to reproduce complex features that could not be generated with traditional kriging.     

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.     

地质统计学在气象要素场插值的实例研究

对两种气象要素场数据分别用距离平方反比法、三次B样条和克里格（Kriging）法插值计算.比较了三种方法结果的差异和当计算场满足不同类型克里格数学假设前提下,普通克里格法（OK）与泛克里格法（UK）插值结果的异同.结果表明：克里格法的误差普遍偏小,且在插值区域峰值处克里格法的最大绝对误差和残差方差均可能较样条的小,说明只要充分了解研究区域特点,恰当选用参数,克里格法有可能得到优于样条的结果,而距离平方反比法和克里格法用全场数据插值不如使用局部数据插值的精度高,则表明内插计算具有局域性.同时还发现,虽然插值场是否满足克里格法假设对插值结果存在影响,但这种影响有时并不重要,它依赖于插值场的性质.     

Spatial assessment of fishing effort around European marine reserves: implications for successful fisheries management

We examined the spatial dynamic of artisanal fishing fleets around five European marine protected areas (MPAs) to derive general implications for the evaluation of MPAs as fisheries management tools. The coastal MPAs studied were located off France, Malta and Spain and presented a variety of spatial designs and processes of establishment. We developed a standardized methodology to define factors influencing effort allocation and to produce fishing effort maps by merging GIS with geostatistical modelling techniques. Results revealed that in most cases the factors “distance to the no-take”, “water depth”, and “distance to the port” had a significant influence on effort allocation by the fishing fleets. Overall, we found local concentration of fishing effort around the MPA borders. Thus, neglecting the pattern of fishing effort distribution in evaluating MPA benefits, such as spillover of biomass, could hamper sound interpretation of MPAs as fisheries management tools.     

模糊类别制图的空间统计学方法

类别地图是地理信息系统（ＧＩＳ）应用中所利用的重要数据类别。这类数据可以从摄影测量和遥感技术得到。用摄影测量方法（影像判读）制作的类别地图常以点、线和多边形的离散目标形式描述,而遥感图像分类方法输出的类别地图以连通光栅块形式表达。不论哪一种情况,在每一个多边形或者光栅块（即制图单元）中仅允许单一类别,边界内部非均匀性和模糊形已经被“过滤”了。这样的类别地图沿用了古曲脆集合论,因为每个制图单元只允许     

Spatial and temporal study of nitrate concentration in groundwater by means of coregionalization

 Spatial and temporal behavior of hydrochemical parameters in groundwater can be studied using tools provided by geostatistics. The cross-variogram can be used to measure the spatial increments between observations at two given times as a function of distance (spatial structure). Taking into account the existence of such a spatial structure, two different data sets (sampled at two different times), representing concentrations of the same hydrochemical parameter, can be analyzed by cokriging in order to reduce the uncertainty of the estimation. In particular, if one of the two data sets is a subset of the other (that is, an undersampled set), cokriging allows us to study the spatial distribution of the hydrochemical parameter at that time, while also considering the statistical characteristics of the full data set established at a different time. This paper presents an application of cokriging by using temporal subsets to study the spatial distribution of nitrate concentration in the aquifer of the Lucca Plain, central Italy. Three data sets of nitrate concentration in groundwater were collected during three different periods in 1991. The first set was from 47 wells, but the second and the third are undersampled and represent 28 and 27 wells, respectively. Comparing the result of cokriging with ordinary kriging showed an improvement of the uncertainty in terms of reducing the estimation variance. The application of cokriging to the undersampled data sets reduced the uncertainty in estimating nitrate concentration and at the same time decreased the cost of the field sampling and laboratory analysis. Received: 23 July 1997 · Accepted: 31 March 1998     

Conditional simulation of intrinsic random functions of order k

Conditional simulation of intrinsic random functions of orderk is a stochastic method that generates realizations which mimic the spatial fluctuation of nonstationary phenomena, reproduce their generalized covariance and honor the available data at sampled locations. The technique proposed here requires the following steps: (i) on-line simulation of Wiener-Levy processes and of their integrations; (ii) use of the turning-bands method to generate realizations in Rⁿ; (iii) conditioning to available data; and (iv) verification of the reproduced generalized covariance using generalized variograms. The applicational aspects of the technique are demonstrated in two and three dimensions. Examples include the conditional simulation of geological variates of the Crystal Viking petroleum reservoir, Alberta, Canada.