Statistical process control in the evaluation of geostatistical simulations

This paper deals with a question: how many stochastic realizations of sequential Gaussian and indicator simulations should be generated to obtain a fairly stable description of the studied spatial process? The grids of E-type estimations and conditional variances were calculated from pooled sets of 100 realizations (the cardinality of the subsets increases by one in the consecutive steps). At each pooling step, a grid average was derived from the corresponding E-type grid, and the variance (calculated for all the simulated values of the pooling set) was decomposed into within-group variance (WGV) and between-group variance (BGV). The former was used as a measurement of numerical uncertainty at grid points, while the between-group variance was regarded as a tool to characterize the geologic heterogeneity between grid nodes. By plotting these three values (grid average, WGV, and BGV) against the number of pooling steps, three equidistant series could be defined. The ergodic fluctuations of the stochastic realizations may result in some “outliers” in these series. From a particular lag, beyond which no “outlier” occurs, the series can be regarded as being fully controlled by a background statistical process. The number of pooled realizations belonging to this step/lag can be regarded as the sufficient number of realizations to generate. In this paper, autoregressive integrated moving average processes were used to describe the statistical process control. The paper also studies how the sufficient number of realizations depends on grid resolutions. The method is illustrated on a computed tomography slice of a sandstone core sample

Sedimentologic modelling of the Ap-13 hydrocarbon reservoir

Abstract Over the years many studies have been conducted to understand the delta system of the Algyő field, many of them dealing with the Ap-13 reservoir. In the present study, therefore, several papers have been reviewed and analyzed to provide the basis for a more detailed description of this reservoir. A macro-scale sedimentological model was developed using Markov analysis. Golden Software's Surfer 8.1 and Strater were used to construct the maps and to define the vertical sedimentological facies of the A-993 borehole. The mega-scale sedimentological 3-D model and the petrophysical parameters of 144 boreholes were analyzed using the Rockware RockWorks 15 and SPSS software. It is concluded, when comparing the vertical section of the A-993 borehole (from the core description) with the sand content from the 3-D model at similar depth, considering the results of the embedded Markov model and the 3-D sedimentological model, that the reservoir is a deep-marine sand body, with a sand content less than 55% and siltstone content of around 30%. It is characterized by the features of proximal middle fan systems

Characterizing sedimentary processes in abandoned channel using compositional data analysis and wavelet transform

Grain size distribution (GSD) is essential for characterizing the deposition process. However, it is necessary to consider its compositional constraint to comprehend the statistical distribution of size fractions within the sediments. Compositional data analysis (CoDA) and wavelet transform (WT) represent alternative methods beyond traditional approaches, e.g., probability density function (PDF). This paper introduces a quantitative approach for characterizing Quaternary depositional and environmental changes using abandoned channel infill sediments. The proposed approach integrates CoDA and WT to thoroughly comprehend the depositional patterns observed in abandoned channels and the underlying environmental variability. The depositional model constructed based on CoDA showed coarsening-upward sequences, suggesting a periodic connection between the main channel and the oxbow lake. Three scales of cycles consistent with the depositional model constructed using CoDA were identified based on WT: small, medium, and large-scale cycles of processes. The large-scale cycles indicate the main depositional events, while the medium and small scale reflects the variation within and during deposition. CoDA and WT demonstrate excellent potential in characterizing the GSD and interpreting oxbow lakes' deposition and sedimentation processes

Cluster defined sedimentary elements of deep-water clastic depositional systems and their 3D spatial visualization using parametrization: a case study from the Pannonian-basin

Many multivariate statistical techniques have the ability to handle large data sets or a great number of parameters. Therefore, these multivariate statistical approaches are widely used in clastic sedimentology for facies analysis. Furthermore, most of the techniques which try to separate more or less homogeneous subsets can be subjective. This subjectivity raises several questions about the significance and confidence of clustering. The goal of this study is to optimize clustering and to evaluate the proper number of clusters needed in order to describe sedimentary and lithological facies through common characteristics. Also, with the interpretation of the clusters, the parametrized geometry adds further but quasi-subjective information to a 3D geologicalmodel. Two assumptions must be met: (1) well-definable geometries must correspond to the architectural elements (2) it is assumed that exactly one sedimentary or lithological facies belongs to each structural element and the flow properties are determined by these structural elements. This approach was applied to the clastic depositional data from a Miocene hydrocarbon reservoir (Algyő field, Hungary) to demonstrate the fidelity of the clustering method yielding an optimum of five cluster facies. The revealed clusters represent lithological characteristics within a (delta fed) submarine fan system. The paper deals with two stressed clusters in particular, showing sinusoid channels which were recognizable and measureable using parametrisation.</p

The advantages of using sequential stochastic simulations when mapping small-scale heterogeneities of the groundwater level

In the environmental risk assessment of oil fields, a detailed knowledge of the heterogeneity of groundwater surfaces is absolutely indispensable. Based on theoretical considerations, in order to analyse small-scale heterogeneities, we decided that the Sequential Gaussian Simulation (SGS) approach seemed to be the most appropriate one. This method gives preference to the reproduction of small-scale heterogeneities at the expense of local accuracy. To test whether this kind of heterogeneity of the groundwater level corresponds to sedimentological variability, a point bar of the River Tisza (South-Hungary) was chosen. In variograms, the longest range was derived from the large-scale sedimentological heterogeneity of the point-bar, the medium range was in accordance with the radius of the meander and its direction coincided with the depositional strike of the meander, while the shortest range corresponded to the lateral heterogeneity of the deposits where the ground water level was measured. The similarities and differences of the realizations of SGS express the uncertainty of the map representation of the ground water surface. The E-type estimates of 100 equiprobable realizations resulted in a very detailed surface. The hydraulic gradient map obtained from the E-type estimates can provide us with a better understanding of the local flow characteristics

The Advantages of Using Sequential Stochastic Simulations when Mapping Small-Scale Heterogeneities of the Groundwater Level

In the environmental risk assessment of oil fields, a detailed knowledge of the heterogeneity of groundwater surfaces is absolutely indispensable. Based on theoretical considerations, in order to analyse small-scale heterogeneities, we decided that the Sequential Gaussian Simulation (SGS) approach seemed to be the most appropriate one. This method gives preference to the reproduction of small-scale heterogeneities at the expense of local accuracy. To test whether this kind of heterogeneity of the groundwater level corresponds to sedimentological variability, a point bar of the River Tisza (South-Hungary) was chosen. In variograms, the longest range was derived from the large-scale sedimentological heterogeneity of the point-bar, the medium range was in accordance with the radius of the meander and its direction coincided with the depositional strike of the meander, while the shortest range corresponded to the lateral heterogeneity of the deposits where the ground water level was measured. The similarities and differences of the realizations of SGS express the uncertainty of the map representation of the ground water surface. The E-type estimates of 100 equiprobable realizations resulted in a very detailed surface. The hydraulic gradient map obtained from the E-type estimates can provide us with a better understanding of the local flow characteristics

Annual mean urban heat island versus 2D surface parameters : modelling, validation and extension

Our assumption is that the mean daily maximum heat island of towns situated on a plain can be assessed on the basis of their surface features. Based on temperature and surface cover data from Szeged and Debrecen, the aim of our research is to construct a multiple variable model for estimating the spatial distribution of the mean heat island, the validation of this model and then to extend our results to other towns situated in a similar environment with no temperature measurements available