Geostatistical seismic inversion and 3D modelling of metric flow units,porosity and permeability in Brazilian presalt reservoir

Flow units(FU)rock typing is a common technique for characterizing reservoir flow behavior,producing reliable porosity and permeability estimation even in complex geological settings.However,the lateral extrapolation of FU away from the well into the whole reservoir grid is commonly a difficult task and using the seismic data as constraints is rarely a subject of study.This paper proposes a workflow to generate numerous possible 3D volumes of flow units,porosity and permeability below the seismic resolution limit,respecting the available seismic data at larger scales.The methodology is used in the Mero Field,a Brazilian presalt carbonate reservoir located in the Santos Basin,who presents a complex and heterogenic geological setting with different sedimentological processes and diagenetic history.We generated metric flow units using the conventional core analysis and transposed to the well log data.Then,given a Markov chain Monte Carlo algorithm,the seismic data and the well log statistics,we simulated acoustic impedance,decametric flow units(DFU),metric flow units(MFU),porosity and permeability volumes in the metric scale.The aim is to estimate a minimum amount of MFU able to calculate realistic scenarios porosity and permeability scenarios,without losing the seismic lateral control.In other words,every porosity and permeability volume simulated produces a synthetic seismic that match the real seismic of the area,even in the metric scale.The achieved 3D results represent a high-resolution fluid flow reservoir modelling considering the lateral control of the seismic during the process and can be directly incorporated in the dynamic characterization workflow.

Three-dimensional Modeling of Ore-forming Elements and Mineralization Prognosis for the Yechangping Mo Deposit,Henan Province,China

Three-dimensional geochemical modeling of ore-forming elements is crucial for predicting deep mineralization.This approach provides key information for the quantitative prediction of deep mineral localization,three-dimensional fine interpolation,analysis of spatial distribution patterns,and extraction of quantitative mineral-seeking markers.The Yechangping molybdenum(Mo)deposit is a significant and extensive porphyry-skarn deposit in the East Qinling-Dabie Mo polymetallic metallogenic belt at the southern margin of the North China Block.Abundant borehole data on oreforming elements underpin deep geochemical predictions.The methodology includes the following steps:(1)Threedimensional geological modeling of the deposit was established.(2)Correlation,cluster,and factor analyses post delineation of mineralization stages and determination of mineral generation sequence to identify(Cu,Pb,Zn,Ag)and(Mo,W,mfe)assemblages.(3)A three-dimensional geochemical block model was constructed for Mo,W,mfe,Cu,Zn,Pb,and Ag using the ordinary kriging method,and the variational function was developed.(4)Spatial distribution and enrichment characteristics analysis of ore-forming elements are performed to extract geological information,employing the variogram and w(Cu+Pb+Zn+Ag)/w(Mo+W)as predictive indicators.(5)Identifying the western,northwestern,and southwestern areas of the mine with limited mineralization potential,contrasted by the northeastern and southeastern areas favorable for mineral exploration.

Groundwater quality assessment using multivariate analysis,geostatistical modeling, and water quality index(WQI): a case of study in the Boumerzoug-El Khroub valley of Northeast Algeria

In this study,the analytical data set of 26 groundwater samples from the alluvial aquifer of Boumerzoug-E1 khroub valley has been processed simultaneously with Multivariate analysis,geostatistical modeling,WQI,and geochemical modeling.Cluster analysis identified three main water types based on the major ion contents,where mineralization increased from group 1 to group 3.These groups were confirmed by FA/PCA,which demonstrated that groundwater quality is influenced by geochemical processes(water-rock interaction)and human practice(irrigation).The exponential semivariogram model WQI.Groundwater chemistry has a strong spatial structure for Mg,Na,Cl,and NO3,and a moderate spatial structure for EC,Ca,K,HCO3,and SO4.Water quality maps generated using ordinary Kriging are consistent with the HCA and PCA results.All water groups are supersaturated with respect to carbonate minerals,and dissolution of kaolinite and Ca-smectite is one of the processes responsible for hydrochemical evolution in the area.

Geostatistical Methods for Lithological Aquifer Characterization and Groundwater Flow Modeling of the Catania Plain Quaternary Aquifer (Italy)

Sedimentary heterogeneity conditions of Catania Plain quaternary aquifer (CPQA), the wider alluvial multi-aquifer system of Sicily, were rebuilt to simulate and quantify groundwater flow. Transition probabilities based on a Markov Chain (MC) and Sequential Indicator Simulation (SIS) are the structure-imitating simulators utilized for generating stochastic distributions of hydraulic conductivity fields of CPQA, basing on borehole data: plausible equiprobable solutions of the complex geological structure of the CPQA were simulated. This study highlights that the choice of geostatistical simulation method plays a fundamental role in predictive scenarios for groundwater resources managing of CPQA. Indeed, simulated characteristics of the sedimentary heterogeneity constituted the basis of finite difference models for simulating the groundwater flow of CPQA. In heterogeneous systems such as CPQA, SIS may be inadequate for reproducing the macrostructures. Instead, MC adequately reproduced spatial connection of lithofacies, representing a more realistic solution dealing to the proposed geological model of CPQA. MC and SIS models were utilized to both assess the uncertainty of the generated hydraulic conductivity fields of CPQA and predictions about its behavior under normal stress conditions induced by urbanization. The calibration of CPQA groundwater flow models based on MC and SIS simulations allowed to achieve a realistic feedback about the quality of the geostatistical reconstructions of the geological heterogeneity field.

Geostatistical Modeling of Uncertainty for the Risk Analysis of a Contaminated Site

This work is a study of multivariate simulations of pollutants to assess the sampling uncertainty for the risk analysis of a contaminated site. The study started from data collected for a remediation project of a steel- works in northern Italy. The soil samples were taken from boreholes excavated a few years ago and analyzed by a chemical laboratory. The data set comprises concentrations of several pollutants, from which a subset of ten organic and inorganic compounds were selected. The first part of study is a univariate and bivariate sta- tistical analysis of the data. All data were spatially analyzed and transformed to the Gaussian space so as to reduce the effects of extreme high values due to contaminant hot spots and the requirements of Gaussian simulation procedures. The variography analysis quantified spatial correlation and cross-correlations, which led to a hypothesized linear model of coregionalization for all variables. Geostatistical simulation methods were applied to assess the uncertainty. Two types of simulations were performed: correlation correction of univariate sequential Gaussian simulations (SGS), and sequential Gaussian co-simulations (SGCOS). The outputs from the correlation correction simulations and SGCOS were analyzed and grade-tonnage curves were produced to assess basic environmental risk.

Spatial Modeling of Soil Lime Requirements with Uncertainty Assessment Using Geostatistical Sequential Indicator Simulation

This work presents and analyses a geostatistical methodology for spatial modelling of Soil Lime Requirements (SLR) considering punctual samples of Cation Exchange Capacity (CEC) and Base Saturation (BS) soil properties. Geostatistical Sequential Indicator Simulation is used to draw realizations from the joint uncertainty distributions of the CEC and the BS input variables. The joint distributions are accomplished applying the Principal Component Analyses (PCA) approach. The Monte Carlo method for handling error propagations is used to obtain realization values of the SLR model which are considered to compute and store statistics from the output uncertainty model. From these statistics, it is obtained predictions and uncertainty maps that represent the spatial variation of the output variable and the propagated uncertainty respectively. Therefore, the prediction map of the output model is qualified with uncertainty information that should be used on decision making activities related to the planning and management of environmental phenomena. The proposed methodology for SLR modelling presented in this article is illustrated using CEC and BS input sample sets obtained in a farm located in Ponta Grossa city, Paraná state, Brazil.

A training image optimization method in multiple-point geostatistics and its application in geological modeling

Based on the analysis of the high-order compatibility optimization method proposed by predecessors, a new training image optimization method based on data event repetition probability is proposed. The basic idea is to extract the data event contained in the condition data and calculate the number of repetitions of the extracted data events and their repetition probability in the training image to obtain two statistical indicators, unmatched ratio and repeated probability variance of data events. The two statistical indicators are used to characterize the diversity and stability of the sedimentary model in the training image and evaluate the matching of the geological volume spatial structure contained in data of the well block to be modeled. The unmatched ratio reflects the completeness of geological model in training image, which is the first choice index. The repeated probability variance reflects the stationarity index of geological model of each training image, and is an auxiliary index. Then, we can integrate the above two indexes to achieve the optimization of training image. Multiple sets of theoretical model tests show that the training image with small variance and low no-matching ratio is the optimal training image. The method is used to optimize the training image of turbidite channel in Plutonio oilfield in Angola. The geological model established by this method is in good agreement with the seismic attributes and can better reproduce the morphological characteristics of the channels and distribution pattern of sands.

The Application of Geostatistical Methods to Prepare the 3D Petrophysical Model of Oil Reservoir

In this study, the petrophysical parameters such as density, sonic, neutron, and porosity were investigated and presented in the 3D models. The 3D models were built using geostatistical method that is used to estimate studied parameters in the entire reservoir. For this purpose, the variogram of each parameter was determined to specify spatial correlation of data. Resulted variograms were non-monotonic. That shows anisotropy of structure. The lithology and porosity parameters are the main causes of this anisotropy. The 3D models also show that petrophysical data has higher variation in north part of reservoir than south part. In addition to, the west limb of reservoir shows higher porosity than east limb. The variation of sonic and neutron data are similar whereas the density data has opposed variation.

A GIS-based time-dependent seismic source modeling of Northern Iran

： The first step in any seismic hazard study is the definition of seismogenic sources and the estimation of magnitude-frequency relationships for each source. There is as yet no standard methodology for source modeling and many researchers have worked on this topic. This study is an effort to define linear and area seismic sources for Northern Iran. The linear or fault sources are developed based on tectonic features and characteristic earthquakes while the area sources are developed based on spatial distribution of small to moderate earthquakes. Time-dependent recurrence relationships are developed for fault sources using renewal approach while time-independent frequency-magnitude relationships are proposed for area sources based on Poisson process. GIS functionalities are used in this study to introduce and incorporate spatial- temporal and geostatistical indices in delineating area seismic sources. The proposed methodology is used to model seismic sources for an area of about 500 by 400 square kilometers around Tehran. Previous researches and reports are studied to compile an earthquake/fault catalog that is as complete as possible. All events are transformed to uniform magnitude scale; duplicate events and dependent shocks are removed. Completeness and time distribution of the compiled catalog is taken into account. The proposed area and linear seismic sources in conjunction with defined recurrence relationships can be used to develop time-dependent probabilistic seismic hazard analysis of Northern Iran.

Research on 3D Distribution of Meandering River Sand Body Using Sedimentary Facies Method and 3D Geological Modeling

Sedimentary facies study is an important method in describing the property and distribution of reservoir. 3D geological modeling is a powerful tool in 3D characterization of geological bodies. By combining the sedimentary facies study with 3D geological modeling to generate 3D sedimentary facies model, the 3D geometry and distribution feature of sand bodies can be more accurately characterized, particularly in 3D view. In Liuchu oilfield of Jizhong depression, the Ed2IV formation was recognized as meandering river deposition facies and five sedimentary facies were identified, which include point bar sand, levee, channel margin, abandoned channel and floodplain. All the 24 sand body facies in Ed2IV were mapped and the 3D sedimentary facies model established based on 2D facies maps. The result shows that the 3D sedimentary facies model is well matched for the research result of sedimentary facies. Being an extension of traditional sedimentary study, the 3D sedimentary facies model can be used to describe the 3D geometry and distribution orders of a single sand body more reliably and more accurately.

Quantifying the impact of mineralogical heterogeneity on reactive transport modeling of CO_(2)+O_(2) in-situ leaching of uranium

CO_(2)+O_(2) in-situ leaching(ISL)of sandstonetype uranium ore represents the third generation of solution mining in China.In this study,reactive transport modeling of the interaction between hydrodynamic and geochemical reactions is performed to enable better prediction and regulation of the CO_(2)+O_(2) in-situ leaching process of uranium.Geochemical reactions between mining solutions and rock,and the kinetic uranium dissolution controlled by O_(2)(aq)and bicarbonate(HCO_(3)-)are considered in the CO_(2)+O_(2) ISL reactive transport model of a typical sandstone-hosted uranium ore deposit in northern China.The reactive leaching of uranium is most sensitive to the spatial distribution of the mineralogical properties of the uranium deposit.Stochastic geostatistical models are used to represent the uncertainty on the spatial distribution of mineral grades.A Monte Carlo analysis was also performed to simulate the uranium production variability over an entire set of geostatistical realizations.The ISL stochastic simulation performed with the selected geostatistical realizations approximates the uranium production variability well.The simulation results of the ISL reactive transport model show that the extent of the uranium plume is highly dependent on mineralogical heterogeneity.The uncertainty analysis suggests the effect of uranium grade heterogeneity was found to be important to improve the accurate capture of the uncertainty.This study provides guidance for the accurate simulation and dynamic regulation of the CO_(2)+O_(2) leaching process of uranium at the scale of large mining areas.

Facets of Uncertainty in Digital Elevation and Slope Modeling

This paper investigates the differences that result from applying different approaches to uncertainty modeling and reports an experimental examining error estimation and propagation in elevation and slope, with the latter derived from the former. It is confirmed that significant differences exist between uncertainty descriptors, and propagation of uncertainty to end products is immensely affected by the specification of source uncertainty.

基于Geostatistical Analyst的喀斯特地区土壤养分空间变异研究

基于ARCGIS平台Geostatistical Analyst模块对喀斯特地区土壤养分空间变异特征进行研究,以贵州省黔西县韦寨村为研究区,首先对研究区内耕地土壤进行取样,深度为0～ 20cm,并将研究区划分为两片,采样方式分别为25m＊ 25m和50m＊ 50m.通过实验得出土壤中全氮、有效磷、速效钾、有机质含量和pH值.采用GIS地统计分析和常规统计方法对土壤pH值及养分（全氮、有效磷、速效钾、有机质）的空间变异分析和合理采样数目研究.结果表明,研究区内全氮、有效磷、速效钾、pH、有机质均呈对数正态分布;全氮、有效磷、速效钾、pH、有机质均为中等变异强度;研究区内最优采样方式为50m＊ 50m.

Three-Dimensional Reservoir Modeling Using Stochastic Simulation, a Case Study of an East African Oil Field

This paper presents a three-dimensional geological reservoir model created using stochastic simulation. The oil field presented is an East African oil field formed by a structural trap. Data analysis and transformations were conducted on the properties before simulation. The variogram was used to measure the spatial correlation of cell-based facies modeling, and porosity and permeability modeling. Two main lithologies were modelled using sequential indicator simulation, sand and shale. Sand had a percentage of 26.8% and shale of 73.2%. There was a clear property distribution trend of sand and shale from the southwest to the northeastern part of a reservoir. The distribution trend of the facies resembled the proposed depositional model of the reservoir. Simulations show that average porosity and permeability of the reservoir are about 20% and 1004 mD, respectively. Average water saturation was 64%. STOIIP volume of 689.42 MMbbls was calculated. The results of simulation showed that the south eastern part of the reservoir holds higher volumes of oil. In conclusion, the model gave a better geological understanding of the geology of the area and can be used for decision making about the future development of the reservoir, prediction performance and uncertainty analysis.

Iterative static modeling of channelized reservoirs using history-matched facies probability data and rejection of training image

Most inverse reservoir modeling techniques require many forward simulations, and the posterior models cannot preserve geological features of prior models. This study proposes an iterative static modeling approach that utilizes dynamic data for rejecting an unsuitable training image(TI) among a set of TI candidates and for synthesizing history-matched pseudo-soft data. The proposed method is applied to two cases of channelized reservoirs, which have uncertainty in channel geometry such as direction, amplitude, and width. Distance-based clustering is applied to the initial models in total to select the qualified models efficiently. The mean of the qualified models is employed as a history-matched facies probability map in the next iteration of static models. Also, the most plausible TI is determined among TI candidates by rejecting other TIs during the iteration. The posterior models of the proposed method outperform updated models of ensemble Kalman filter(EnKF) and ensemble smoother(ES) because they describe the true facies connectivity with bimodal distribution and predict oil and water production with a reasonable range of uncertainty. In terms of simulation time, it requires 30 times of forward simulation in history matching, while the EnKF and ES need 9000 times and 200 times, respectively.

Algebraic equation of motion approach for solving the Anderson model

Based on the algebraic equation of motion(AEOM)approach,we have studied the single-impurity Anderson model by analytically solving the AEOM of the f-electron one-particle Green function in the Kondo limit.The related spectral function satisfies the sum rule and shows that there is a well-known three-peak structure at zero temperature.In the low energy limit,we obtain the analytical formula of the Kondo temperature that is the same as the exact solution in form except for a prefactor.We also show that the shape of the Kondo resonance is the Lorentzian form and the corresponding weight is proportional to the spin-flip correlation function.

A Hybrid Geostatistical Method for Estimating Citywide Traffic Volumes - A Case Study of Edmonton, Canada

Traffic volume information has long played an important role in many transportation related works,such as traffic operations,roadway design,air quality control,and policy making.However,monitoring traffic volumes over a large spatial area is not an easy task due to the significant amount of time and manpower required to collect such large-scale datasets.In this study,a hybrid geostatistical approach,named Network Regression Kriging,has been developed to estimate urban traffic volumes by incorporating auxiliary variables such as road type,speed limit,and network accessibility.Since standard kriging is based on Euclidean distances,this study implements road network distances to improve traffic volumes estimations.A case study using 10-year of traffic volume data collected within the city of Edmonton was conducted to demonstrate the robustness of the model developed herein.Results suggest that the proposed hybrid model significantly outperforms the standard kriging method in terms of accuracy by 4.0%overall,especially for a large-scale network.It was also found that the necessary stationarity assumption for kriging did not hold true for a large network whereby separate estimations for each road type performed significantly better than a general estimation for the overall network by 4.12%.

基于DSM的城市公园对PM_(2.5)和PM_(10)的消减特征研究——以南昌市人民公园为例

【目的】PM_(2.5)、PM_(10)等空气颗粒物是城市空气首要污染物,在城市空气污染中占主导地位。了解固定外源下PM_(2.5)、PM_(10)在城市绿地的消减特征,可为城市阻控空气颗粒物、缓解空气污染提供有利依据。然而目前空气颗粒物的研究大多以点测定方式量化空间结构及植被类型对空气颗粒物的影响,对固定外源污染下PM_(2.5)、PM_(10)在城市绿地空间尺度上的影响机制研究较少。【方法】研究结合DSM与地统计学,以南昌市人民公园为例,探索城市公园阻隔外源污染的空间梯度效应及空间结构类型差异。利用克里金插值法对其空间分布特征进行可视化模拟;利用Arcgis和R语言等软件分析不同空间结构PM_(2.5)、PM_(10)的浓度差异。【结果】人民公园PM_(2.5)、PM_(10)的浓度在空间分布上趋势一致,均表现为以固定外源点为核心,浓度随距离增加呈极显著梯度递减的趋势,且在中部(约距外源点150~220 m处)消减效率最高,约为全园PM_(2.5)平均消减值的7.5倍,PM_(10)平均消减值的3.8倍;PM_(2.5)、PM_(10)受多种因子影响:与空气温度、距离(主导因子)显著负相关、与相对湿度显著正相关,且PM_(2.5)、PM_(10)对不同因子响应特征存在差异;城市公园不同绿地空间结构对PM_(2.5)、PM_(10)的消减及扩散作用差异显著,受其双重影响,PM_(2.5)、PM_(10)的浓度表现为水体>广场>树林>草坪,其中PM_(2.5)受影响更显著;此外,受各因子和绿地空间结构耦合影响,部分区域PM_(2.5)、PM_(10)分布异常。【结论】以固定外源点为核心,PM_(2.5)、PM_(10)浓度随距离增加呈极显著梯度递减的趋势,且在中部消减效率最高;PM_(2.5)、PM_(10)浓度与相对湿度显著正相关,与空气温度与距离显著负相关,其中PM_(10)对距离和相对湿度响应较为明显,而PM_(2.5)受空气温度影响较大;在随距离变化基础上,不同城市绿地空间结构对PM_(2.5)、PM_(10)消减和扩散作用差异导致了局部分布差异。

基于PSO-Kriging算法的三维地质建模技术研究

三维地质模型的构建对于理解和预测地下结构至关重要。地质钻孔数据能够反映岩体空间分布和地质构造特征,本研究以小保当一号煤矿11盘区内的23个地质钻孔数据为基础,采用添加虚拟地层的方法解决了地层缺失与地层重复现象,构建共计27层地层的三维地质模型以及二维剖面模型。此外,针对传统的克里金方法在处理复杂地质数据参数选择困难的问题,采用粒子群算法对传统克里金插值方法中的块金值(C 0)、偏基台值(C)和变程(a)三个关键参数进行寻优,从而克服普通克里金插值参数选择的主观性和不确定性,采用实际验证法选取了研究区内四个钻孔来对比插值结果,结果表明经过PSO优化的Kriging算法在X3-1、X3-2、K3-4、K3-5四个钻孔的RMSE值分别降低至1.184、1.267、1.606、1.560,相比于Kriging的RMSE平均降低了31%,且PSO-Kriging算法在四个钻孔处对2-2煤层的插值结果与实际值相比较误差分别为1.00 m、0.01 m、0.11 m和0.03 m,比Kriging插值结果更接近实际值,表明了所提方法的有效性和优越性。

尖灭分叉型煤层三维地质建模研究:基于地质统计学和符号矩阵的方法

由于成煤期的泥炭沼泽基底不平以及地质环境等的变化,导致相对较大的地质区域内煤层常出现尖灭、分叉等复杂情况,影响开采设计,为高效准确定位煤层边界及分布位置,提出一种基于地质统计学和符号矩阵进行三维地质建模的方法。通过符号矩阵方法,按照一定精度离散煤层和非煤层数据,利用泛克里金法确定平面煤层厚度,反距离加权法确定每个栅格的符号距离函数估值,局部窗口对煤层进行精准定位,确定与煤层厚度相匹配的距离函数截距,建立煤层的三维地质模型,并讨论了距离函数截距对煤层精度的影响;滑动垂直窗口大小与煤层位置对建模结果中煤层连通性的影响。结果表明:该建模方法可以针对煤层尖灭、分叉等复杂情况快速建模,对大范围区域地质模型构建有一定的适用性,自动化程度高,可应用于煤层开采设计及资源评估。