Conditional simulation as a tool for measuring uncertainties in petroleum exploration

Despite its flexibility when compared with parametric methods, there are significant problems with sequential indicator simulation (SIS) for continuous variables. These come from the successive construction of the local conditional distributions by indicator kriging and the use of Monte–Carlo simulation for sampling the simulated values from such distributions. Some problems of SIS have been addressed satisfactorily; order relation deviations and the extrapolation of the distribution tails are manageable. The most important outstanding challenges are: (1) there is no resolution within a grade range, and (2) there is no correlation between different grade ranges. These problems lead to an over-smoothing of grades and a reduced, but misleading, uncertainty when point scale simulations are average up at the selective mining unit size. Attempting to account for the interclass correlation by cokriging fails because there is no adequate model for fitting the complete matrix of indicator variograms. Also, attempting to improve the within class resolution by using the class edge distance function does not provide a complete solution. In regard of these unresolved challenges, the practitioner is cautioned about the use of SIS of continuous variables for Resource Evaluation. Instead, a combination of categorical variables simulation methods (including SIS) for modeling the mineralisation domains, and Gaussian simulation of grades within these domains is recommended.

O objetivo deste trabalho foi avaliar o desempenho da simulação sequencial gaussiana (SSG) e da simulação sequencial indicatriz (SSI) na modelagem da incerteza das predições do K disponível em área de cana-de-açúcar, e comparar as simulações com o método já consagrado de krigagem ordinária (KO). Uma malha amostral com 626 pontos foi instalada em área de 200 ha, no Município de Tabapuã, em São Paulo. As simulações reproduziram a variabilidade dos dados amostrais de K disponível, enquanto a KO superestimou os baixos teores de K e subestimou os altos. O mapa de desvio-padrão obtido a partir da KO mostrou menor variação ao longo da área de estudo, quando comparado aos mapas obtidos a partir das simulações. A SSI obteve acurácia 22% superior à obtida pela SSG, na modelagem da função de distribuição condicional do K. As simulações apresentam maior eficiência que a KO para modelar incerteza na distribuição espacial do K. A SSI apresenta melhor desempenho que a SSG na estimativa dos teores de K disponível, em área de cana-de-açúcar.

Updating cover type maps using sequential indicator simulation

Flow simulation studies require an accurate model of the reservoir in terms of its sedimentological architecture. Pixel-based reservoir modeling techniques are often used to model this architecture. There are, however, two problem areas with such techniques. First, several statistical parameters have to be provided whose influence on the resulting model is not readily inferable. Second, conditioning the models to relevant geological data that carry great uncertainty on their own adds to the difficulty of obtaining reliable models and assessing model reliability. The Sequential Indicator Simulation (SIS) method has been used to examine the impact of such uncertainties on the final reservoir model. The effects of varying variogram types, frequencies of lithology occurrence, and the gridblock model orientation with respect to the sedimentological trends are illustrated using different reservoir modeling studies. Results indicate, for example, that the choice of variogram type can have a significant impact on the facies model. Also, reproduction of sedimentological trends and large geometries requires careful parameter selection. By choosing the appropriate modeling strategy, sedimentological principles can be translated into the numerical model. Solutions for dealing with such issues and the geological uncertainties are presented. In conclusion, each reservoir modeling study should begin by developing a thorough quantitative sedimentological understanding of the reservoir under study, followed by detailed sensitivity analyses of relevant statistical and geological parameters.

Multiple techniques are available to construct three-dimensional reservoir models. This study uses comparative analysis to test the impact of applying four commonly used stochastic modeling techniques to capture geologic heterogeneity and fluid-flow behavior in fluvial-dominated deltaic reservoirs of complex facies architecture: (1) sequential indicator simulation; (2) object-based modeling; (3) multiple-point statistics (MPS); and (4) spectral component geologic modeling. A reference for comparison is provided by a high-resolution model of an outcrop analog that captures facies architecture at the scale of parasequences, delta lobes, and facies-association belts. A sparse, pseudosubsurface data set extracted from the reference model is used to condition models constructed using each stochastic reservoir modeling technique. Models constructed using all four algorithms fail to match the facies-association proportions of the reference model because they are conditioned to well data that sample a small, unrepresentative volume of the reservoir. Simulated sweep efficiency is determined by the degree to which the modeling algorithms reproduce two aspects of facies architecture that control sand-body connectivity: (1) the abundance, continuity, and orientation of channelized fluvial sand bodies; and (2) the lateral continuity of barriers to vertical flow associated with flooding surfaces. The MPS algorithm performs best in this regard. However, the static and dynamic performance of the models (as measured against facies-association proportions, facies architecture, and recovery factor of the reference model) is more dependent on the quality and quantity of conditioning data and on the interpreted geologic scenario(s) implicit in the models than on the choice of modeling technique.

Modeling the estimation of petroleum resources in the United States

A case study is presented in which a two-stage stochastic modeling approach was employed for modeling heterogeneities in a deep-water Gulf of Mexico field. The hydrocarbon-bearing intervals of this field were deposited as turbidites and exhibit high net sand/gross interval (net/gross) ratios. In the first stage, a new facies indicator geostatistical method was used to model uncertainties associated with facies maps derived from seismic amplitudes. The concept of pseudo-wells is introduced for capturing geologic features and constraining the stochastic realizations. In the second modeling stage, synthetic stratigraphic columns based on whole core descriptions were used to capture fine-scale heterogeneities in cross-sectional panels. These cross-sections were subjected to flow simulations, yielding scaled-up values of single and two-phase flow parameters. Results from both stages were combined into a full-field 3-D reservoir simulation model.

Although the Pannonian Basin in Hungary boasts significant geothermal potential, most geothermal wells in the region suffer from reinjection issues. The aim of this study is to examine the impact of the sedimentary architecture of a paralic lacustrine succession on the static connectivity of a geothermal aquifer. This problem was examined for a case-study geothermal doublet drilled in Mezőberény, southeast Hungary, which experienced injectivity problems shortly after commencing operations in 2012, ultimately leading to shut-in of the wells. A characterization of the architecture of the deltaic aquifer has been undertaken through a novel workflow that combines sedimentological and sequence stratigraphic analysis of the well-doublet and stochastic 3D modelling techniques to assess the likely static connectivity between the production and injection wells. Planform dimension of aquifer-forming mouth-bar elements and fluvial channel bodies were estimated from geological analogues, selected based on the thickness values of such sedimentary bodies interpreted on the gamma-ray logs of the well doublet and nearby hydrocarbon wells. In total five mouth-bar and two fluvial channel input geometry groups were selected, and fifty object-based realizations were constructed to analyse the static connectivity of different geological scenarios. The internal lithology of mouth-bar and fluvial-channel elements were modelled by sequential indicator simulations (ten realizations). Results of connected volume analysis indicate that the sandstone content of the aquifer is located within vertically segmented fluvial-channel and mouth-bar elements separated by mud-prone prodelta and lower delta-front deposits. This architectural configuration, in combination with low net-sandstone content suggests limited connectivity between the wells. Across the set of stochastic realizations, the volume of sandstone connecting the injection and production wells is ∼4% of the total aquifer volume, on average. Results of this study shows that simplified reservoir models can lead to over-estimation of connectivity of geothermal doublets. The proposed workflow combines sedimentological analysis and 3D modelling supported by geological analogues to predict sandstone reservoir connectivity of deltaic geothermal reservoirs. The described workflow can be carried out in target areas using existing boreholes to assist borehole planning.

Estimation of NDVI Images Using Geostatistical Methods

In practical operational studies, facies stochastic modelling is often performed with traditional geostatistical algorithms such as Sequential Indicator Simulation or Truncated Gaussian Simulation. In this presentation, we will focus on recent improvements of geostatistical techniques used to improve geological realism, and we will stress on the key points for their use in operational context. As a basis of discussion for the workshop, we will briefly address: the use and improvements of Multiple Point Statistics; the generalization of Truncated Gaussian Simulation with efficient Pluri- Gaussian Truncation; and the Boolean models with flexible objects.

DSSIM-HR: A FORTRAN 90 program for direct sequential simulation with histogram reproduction

Regional scale inventories of heavy metal concentrations in soil increasingly are being done to evaluate their global patterns of variation. Sometimes these global pattern evaluations reveal information that is not identified by more detailed studies. Geostatistical methods, such as stochastic simulation, have not yet been used routinely for this purpose in spite of their potential. To investigate such a use of geostatistical methods, we analyzed a data set of 14,674 copper and 12,441 cadmium observations in the topsoil of Flanders, Belgium, covering 13,522 km2. Outliers were identified and removed, and the distributions were spatially declustered. Copper was analyzed using sequential Gaussian simulation, whereas for cadmium we used sequential indicator simulation because of the large proportion (43%) of censored data. We complemented maps of the estimated values with maps of the probability of exceeding a critical sanitation threshold for agricultural land use. These sets of maps allowed the identification of regional patterns of increased metal concentrations and provided insight into their potential causes. Mostly areas with known industrial activities (such as lead and zinc smelters) could be delineated, but the effects of shells fired during the First World War were also identified.

A new uncertainty analysis method based on geostatistical simulation and a case study

Description of hydrogeologic heterogeneity and evaluation of radionuclide transport at an underground nuclear test

Simulated annealing optimization technique was used to simulate geological models. After comparing one-point perturbation scheme with two-point swapping scheme, and the Metropolis algorithm with the greedy algorithm, an optimized combination of simulated annealing schedule is presented. The two-dimensional correlation coefficient matrix is introduced to determine a unit configuration which can represent essential features of a geological model. The proposed simulated annealing technique can be used to reproduce the characteristics of a geological model based on multipoint histogram which can be obtained by using a unit configuration. Various geological vertical cross sections and horizontal slices based on field data are used to validate this new technique. Simulated results confirm that one-point perturbation scheme with the Metropolis algorithm provides the best combination to capture the essential features of a geological model. Further, the two-dimensional correlation coefficient matrix provides a technique to choose a priori unit configuration for multipoint histogram, which captures the geological characteristics adequately.