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Geostatistics Toronto 2021

Quantitative Geology and Geostatistics

herausgegeben von: Sebastian Alejandro Avalos Sotomayor, Julian M. Ortiz, R. Mohan Srivastava

Verlag: Springer International Publishing

Buchreihe : Springer Proceedings in Earth and Environmental Sciences

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Über dieses Buch

This open access book provides state-of-the-art theory and application in geostatistics.

Geostatistics Toronto 2021 includes 28 short abstracts, 18 extended abstracts, and 7 full articles in the fields of geostatistical theory, multi-point statistics, earth sciences, mining, optimal drilling, domains, seismic, classification uncertainty risk, and artificial intelligence and machine learning. All contributions were presented at the 11th International Geostatistics Congress held in virtually at Toronto, Canada, from July 12-16, 2021.

This book is valuable to researchers, scientists, and practitioners in geology, mining, petroleum, geometallurgy, mathematics, and statistics.

Inhaltsverzeichnis

Frontmatter

Theory

Frontmatter

Open Access

A Geostatistical Heterogeneity Metric for Spatial Feature Engineering
Abstract
Heterogeneity is a vital spatial feature for subsurface resource recovery predictions, such as mining grade tonnage functions, hydrocarbon recovery factor, and water aquifer draw-down predictions. Feature engineering presents the opportunity to integrate heterogeneity information, but traditional heterogeneity engineered features like Dykstra-Parsons and Lorenz coefficients ignore the spatial context; therefore, are not sufficient to quantify the heterogeneity over multiple scales of spatial intervals to inform predictive machine learning models. We propose a novel use of dispersion variance as a spatial-engineered feature that accounts for heterogeneity within the spatial context, including spatial continuity and sample data and model volume support size to improve predictive machine-learning-based models, e.g., for pre-drill prediction and uncertainty quantification. Dispersion variance is a generalized form of variance that accounts for volume support size and can be calculated from the semivariogram-based spatial continuity model. We demonstrate dispersion variance as a useful predictor feature for the case of hydrocarbon recovery prediction, with the ability to quantify the spatial variation over the support size of the production well drainage radius, given the spatial continuity from the variogram and trajectory of the well. We include a synthetic example based on geostatistical models and flow simulation to show the sensitivity of dispersion variance to production. Then we demonstrate the dispersion variance as an informative predictor feature for production forecasting with a field case study in the Duvernay formation.
Wendi Liu, Léan E. Garland, Jesus Ochoa, Michael J. Pyrcz

Open Access

Iterative Gaussianisation for Multivariate Transformation
Abstract
Multivariate conditional simulations can be reduced to a set of independent univariate simulations through multivariate Gaussian transformation of the drill hole data to independent Gaussian factors. These simulations are then back transformed to obtain simulated results that exhibit the multivariate relationships observed in the input drill hole data. Several transformation techniques are cited in geostatistical literature for multivariate transformation. However, only two can effectively simulate high dimensional drill hole data with complex non-linear features: Flow Anamorphosis (FA) and Projection Pursuit Multivariate Transformation (PPMT). This paper presents an alternative iterative multivariate Gaussian transformation (IG) along with a multivariate simulation case study of a large Nickel deposit. Our findings show that IG is computationally faster than FA and PPMT which makes the technique more appealing for most practical and time-sensitive applications.
A. Cook, O. Rondon, J. Graindorge, G. Booth

Open Access

Comparing and Detecting Stationarity and Dataset Shift
Abstract
Machine learning algorithms have been increasingly applied to spatial numerical modeling. However, it is important to understand when such methods will underperform. Machine learning algorithms are impacted by dataset shift; when modeling domains of interest present non-stationarities there is no guarantee that the trained models are effective in unsampled areas. This work aims to compare the stationarity requirement of geostatistical methods to the concept of dataset shift. Also, workflow is developed to detect dataset shift in spatial data prior to modeling, this involves applying a discriminative classifier and a two sample Kolmogorv-Smirnov test to model areas. And, when required a lazy learning modification of support vector regression is proposed to account for dataset shift. The benefits of the lazy learning algorithm are demonstrated on the well-known non-stationary Walker Lake dataset and improves root mean squared error up to 25% relative to standard SVR approach, in areas where dataset shift is present.
Camilla da Silva, Jed Nisenson, Jeff Boisvert

Open Access

Simulation of Stationary Gaussian Random Fields with a Gneiting Spatio-Temporal Covariance
Abstract
The nonseparable Gneiting covariance has become a standard to model spatio-temporal random fields. Its definition relies on a completely monotone function associated with the spatial structure and a conditionally negative semidefinite function associated with the temporal structure. This work addresses the problem of simulating stationary Gaussian random fields with a Gneiting-type covariance. Two algorithms, in which the simulated field is obtained through a combination of cosine waves are presented and illustrated with synthetic examples. In the first algorithm, the temporal frequency is defined on the basis of a temporal random field with stationary Gaussian increments, whereas in the second algorithm the temporal frequency is drawn from the spectral measure of the covariance conditioned to the spatial frequency. Both algorithms perfectly reproduce the correlation structure with minimal computational cost and memory footprint.
Denis Allard, Xavier Emery, Céline Lacaux, Christian Lantuéjoul

Open Access

Spectral Simulation of Gaussian Vector Random Fields on the Sphere
Abstract
Isotropic Gaussian random fields on the sphere are used in astronomy, geophysics, oceanography, climatology and remote sensing applications. However, to date, there is a lack of simulation algorithms that reproduce the spatial covariance structure without any approximation and, at the same time, are parsimonious in terms of computation time and memory storage requirements. This work presents two such algorithms that rely on the spectral representation of isotropic covariances on the sphere. Both algorithms are illustrated with synthetic examples.
Alfredo Alegría, Xavier Emery, Xavier Freulon, Christian Lantuéjoul, Emilio Porcu, Didier Renard

Petroleum

Frontmatter

Open Access

Geometric and Geostatistical Modeling of Point Bars
Abstract
Point bar reservoir geology is frequently encountered in oil and gas developments worldwide. Furthermore, point bar geology is encountered in many sites being considered for large scale CO2 injection for sequestration. A comprehensive modeling method that adequately preserves point bar internal architecture and its associated heterogeneities is still not available. Traditional geostatistical methods cannot adequately capture the curvilinear architecture of point bars. Even geostatistical simulation techniques that can be constrained to multiple point statistics cannot capture the architecture of the point bars because they use regular grids to represent the heterogeneity. If heterogeneities like the thinly distributed shale drapes within the point bar are represented using an extremely fine mesh, the computational cost for performing flow modeling escalates steeply. This paper proposes a modeling method that preserves the point bar internal architecture and heterogeneities, without these limitations. The modeling method incorporates a gridding scheme that adequately captures the point bar architecture and heterogeneities, without huge computational costs.
Ismael Dawuda, Sanjay Srinivasan

Open Access

Application of Reinforcement Learning for Well Location Optimization
Abstract
The extensive deployment of sensors in oilfield operation and management has led to the collection of vast amounts of data, which in turn has enabled the use of machine learning models to improve decision-making. One of the prime applications of data-based decision-making is the identification of optimum well locations for hydrocarbon recovery. This task is made difficult by the relative lack of high-fidelity data regarding the subsurface to develop precise models in support of decision-making. Each well placement decision not only affects eventual recovery but also the decisions affecting future wells. Hence, there exists a tradeoff between recovery maximization and information gain. Existing methodologies for placement of wells during the early phases of reservoir development fail to take an abiding view of maximizing reservoir profitability, instead focusing on short-term gains. While improvements in drilling technologies have dramatically lowered the costs of producing hydrocarbon from prospects and resulted in very efficient drilling operations, these advancements have led to sub-optimal and haphazard placement of wells. This can lead to considerable number of unprofitable wells being drilled which, during periods of low oil and gas prices, can be detrimental for a company’s solvency. The goal of the research is to present a methodology that builds machine learning models, integrating geostatistics and reservoir flow dynamics, to determine optimum future well locations for maximizing reservoir recovery. A deep reinforcement learning (DRL) framework has been proposed to address the issue of long-horizon decision-making. The DRL reservoir agent employs intelligent sampling and utilizes a reward framework that is based on geostatistical and flow simulations. The implemented approach provides opportunities to insert expert information while basing well placement decisions on data collected from seismic data and prior well tests. Effects of prior information on the well placement decisions are explored and the developed DRL derived policies are compared to single-stage optimization methods for reservoir development. Under similar reward framework, sequential well placement strategies developed using DRL have been shown to perform better than simultaneous drilling of several wells.
Kshitij Dawar, Sanjay Srinivasan, Mort D. Webster

Open Access

Compression-Based Modelling Honouring Facies Connectivity in Diverse Geological Systems
Abstract
In object- or pixel-based modelling, facies connectivity is tied to facies proportion as an inevitable consequence of the modelling process. However, natural geological systems (and rule-based models) have a wider range of connectivity behaviour and therefore are ill-served by simple modelling methods in which connectivity is an unconstrained output property rather than a user-defined input property. The compression-based modelling method decouples facies proportions from facies connectivity in the modelling process and allows models to be generated in which both are defined independently. The two-step method exploits the link between the connectivity and net:gross ratio of the conventional (pixel- or object-based) method applied. In Step 1 a model with the correct connectivity but incorrect facies proportions is generated. Step 2 applies a geometrical transform which scales the model to the correct facies proportions while maintaining the connectivity of the original model. The method is described and illustrated using examples representative of a poorly connected deep-water depositional system and a well-connected fluid-driven vein system.
Tom Manzocchi, Deirdre A. Walsh, Javier López-Cabrera, Marcus Carneiro, Kishan Soni

Open Access

Spatial Uncertainty in Pore Pressure Models at the Brazilian Continental Margin
Abstract
Accurate pore pressure models in wells are essential for ensuring the lowest cost and operational safety during exploration/development projects. This modeling requires the integration of several sources of information such as well data, formation pressure tests, geophysical logs, mud weight, geological models, seismic data, geothermal and sedimentation rate modeling. An empirical relationship between overpressure and compressional wave velocity is commonly applied to model the pore pressure. This deterministic approach does not allow uncertainty quantification and ignores other variables related to pore pressure. This paper presents a case study with real data to evaluate and quantify spatial pore pressure uncertainty. The exhaustive secondary variable came from the combination of seismic velocity and geothermal models. The methodology uses Sequential Gaussian Cosimulation with Intrinsic Collocated Cokriging. The results demonstrate the usefulness and applicability of the workflow proposed.
Felipe Tajá C. Pinto, Krishna Milani, Leandro Guedes, Luiz Eduardo S. Varella, Marcos Fetter, Marcus Santini, Thiago Lopes, Vitor Gorne, Viviane Farroco, Attila L. Rodrigues, João Felipe C. L. Costa, Marcel A. A. Bassani

Open Access

The Suitability of Different Training Images for Producing Low Connectivity, High Net:Gross Pixel-Based MPS Models
Abstract
Pixel-based multiple-point statistical (MPS) modelling is an appealing geostatistical modelling technique as it easily honours well data and allows use of geologically-derived training images to reproduce the desired heterogeneity. A variety of different training image types are often proposed for use in MPS modelling, including object-based, surface-based and process-based models. The purpose of the training image is to provide a description of the geological heterogeneities including sand geometries, stacking patterns, facies distributions, depositional architecture and connectivity. It is, however, well known that pixel-based MPS modelling has difficulty reproducing facies connectivity, and this study investigates the performance of a widely-available industrial SNESIM algorithm at reproducing the connectivity in a geometrically-representative, idealized deep-water reservoir sequence, using different gridding strategies and training images. The findings indicate that irrespective of the sand connectivity represented in the training image, the MPS models have a percolation threshold that is the same as the well-established 27% percolation threshold of random object-based models. A more successful approach for generating poorly connected pixel-based MPS models at high net:gross ratios has been identified. In this workflow, a geometrical transformation is applied to the training image prior to modelling, and the inverse transformation is applied to the resultant MPS model. The transformation is controlled by a compression factor which defines how non-random the geological system is, in terms of its connectivity.
Deirdre A. Walsh, Javier López-Cabrera, Tom Manzocchi

Open Access

Probabilistic Integration of Geomechanical and Geostatistical Inferences for Mapping Natural Fracture Networks
Abstract
Estimation of a reservoir’s production potential, well placement and field development depends largely on accurate modeling of the existing fracture networks. However, there is always significant uncertainty associated with the prediction of spatial location and connectivity of fracture networks due to lack of sufficient data to model them. Therefore, stochastic characterization of these fractured reservoirs becomes necessary.
Akshat Chandna, Sanjay Srinivasan

Mining

Frontmatter

Open Access

Artifacts in Localised Multivariate Uniform Conditioning: A Case Study
Abstract
Localised Multivariate Uniform Conditioning (LMUC) is a technique designed for spatially locating Selective Mining Unit (SMU) grades derived using Multivariate Uniform Conditioning (MUC) for the assessment of recoverable resources. LMUC has the advantage of producing SMU estimates conforming to the MUC panel-specific grade-tonnage curves while preserving the spatial grade distribution at the selective mining level. However, LMUC results have two severe artifacts. This paper documents both artifacts using four grades from a large nickel–cobalt laterite deposit in Western Australia.
Oscar Rondon, Hassan Talebi

Open Access

Methodology for Defining the Optimal Drilling Grid in a Laterite Nickel Deposit Based on a Conditional Simulation
Abstract
In mining projects, the confidence in an estimate is associated with the quantity and quality of the available information. Thus, the closer the data to the targeted location, the smaller the error associated with the estimated value. In the advanced stages of a project (i.e. the pre-feasibility and feasibility phases), it is usual to take samples derived from drillings. Since sampling and chemical analysis involve high costs, it is essential that these costs contribute to a reduction in the uncertainty of estimation. This paper presents a workflow for a case study of a lateritic nickel deposit and proposes a methodology to address the issue of optimising the drilling grid based on uncertainty derived from Gaussian conditional geostatistical simulations. The usefulness of the proposed workflow is demonstrated in terms of saving time and money when selecting a drill hole grid.
Claudia Mara Sperandio Neves, João Felipe Coimbra Leite Costa, Leonardo Souza, Fernando Guimaraes, Geraldo Dias

Open Access

LSTM-Based Deep Learning Method for Automated Detection of Geophysical Signatures in Mining
Abstract
The mining of stratified ore deposits requires detailed knowledge of the location of orebody boundaries. In the Banded Iron Formation (BIF) hosted iron ore deposits located in the Pilbara region of Western Australia the natural gamma logs are useful tool to identify stratigraphic boundaries. However, manually interpreting these features is subjective and time consuming due to the large volume of data. In this study, we propose a novel approach to automatically detect natural gamma signatures. We implemented a LSTM based algorithm for automated detection of signatures. We achieved a relatively high accuracy using gamma sequences with and without added noise. Further, no feature extraction or selection is performed in this work. Hence, LSTM can be used to detect different signatures in natural gamma logs even with noise. So, this system can be introduced in mining as an aid for geoscientists.
Mehala Balamurali, Katherine L. Silversides

Earth Science

Frontmatter

Open Access

Spatio-Temporal Optimization of Groundwater Monitoring Network at Pickering Nuclear Generating Station
Pedram Masoudi, Yvon Desnoyers, Mike Grey

Domains

Frontmatter

Open Access

Applying Clustering Techniques and Geostatistics to the Definition of Domains for Modelling
Abstract
Machine learning is a broad field of study that can be applied in many areas of science. In mining, it has already been used in many cases, for example, in the mineral sorting process, in resource modeling, and for the prediction of metallurgical variables. In this paper, we use for defining estimation domains, which is one of the first and most important steps to be taken in the entire modeling process. In unsupervised learning, cluster analysis can provide some interesting solutions for dealing with the stationarity in defining domains. However, choosing the most appropriate technique and validating the results can be challenging when performing cluster analysis because there are no predefined labels for reference. Several methods must be used simultaneously to make the conclusions more reliable. When applying cluster analysis to the modeling of mineral resources, geological information is crucial and must also be used to validate the results. Mining is a dynamic activity, and new information is constantly added to the database. Repeating the whole clustering process each time new samples are collected would be impractical, so we propose using supervised learning algorithms for the automatic classification of new samples. As an illustration, a dataset from a phosphate and titanium deposit is used to demonstrate the proposed workflow. Automating methods and procedures can significantly increase the reproducibility of the modeling process, an essential condition in evaluating mineral resources, especially for auditing purposes. However, although very effective in the decision-making process, the methods herein presented are not yet fully automated, requiring prior knowledge and good judgment.
Gabriel de Castro Moreira, João Felipe Coimbra Leite Costa, Diego Machado Marques

Open Access

Addressing Application Challenges with Large-Scale Geological Boundary Modelling
Abstract
For banded iron formation-hosted deposits accurate boundary modelling is critical to ore-grade estimation. Key to estimation fidelity is the accurate separation of the different domains within the ore body, requiring modelling of the boundaries between domains. This yields both theoretical and application challenges. We present a series of solutions for application challenges that arise when modelling large-scale boundaries employing a composition of Gaussian Process models on exploration and production hole data. We demonstrate these in the banded iron formation-hosted iron ore deposits in the Hamersley Province of Western Australia. We present solutions to several challenges: the inclusion of information derived from a geologist-defined boundary estimate to incorporate domain knowledge in data sparse regions, the incorporation of unassayed production holes that are implicitly defined as waste to augment production hole assay data, and a more holistic method of defining regional bounds and spatial rotations for Gaussian Process modelling of local spaces. Solution are evaluated against a range of metrics to show performance improvements over the manually performed estimation by an expert geologist of the boundaries delineating the ore body domains. Reconcilliation scores are used for evaluating the quality of predicted domain boundaries against measured production data. The predicted and in situ surfaces are also qualitatively evaluated against production data to ensure that the models were evaluated to be geologically sound by an expert in the field. In particular, better fidelity is shown when separating mineralised and non-mineralised ore, consequently improving the estimation of the ore-grades present in the mine site.
Adrian Ball, John Zigman, Arman Melkumyan, Anna Chlingaryan, Katherine Silversides, Raymond Leung
Backmatter
Metadaten
Titel
Geostatistics Toronto 2021
herausgegeben von
Sebastian Alejandro Avalos Sotomayor
Julian M. Ortiz
R. Mohan Srivastava
Copyright-Jahr
2023
Electronic ISBN
978-3-031-19845-8
Print ISBN
978-3-031-19844-1
DOI
https://doi.org/10.1007/978-3-031-19845-8