Resource Model Updating For Compositional Geometallurgical Variables

In the field of mineral resources extraction, one main challenge is to meet production targets in terms of geometallurgical properties. These properties influence the processing of the ore and are often represented in resource modeling by coregionalized variables with a complex relationship between them. Valuable data are available about geometalurgical properties and their interaction with the beneficiation process given sensor technologies during production monitoring. The aim of this research is to update resource models as new observations become available. A popular method for updating is the ensemble Kalman filter. This method relies on Gaussian assumptions and uses a set of realizations of the simulated models to derive sample covariances that can propagate the uncertainty between real observations and simulated ones. Hence, the relationship among variables has a compositional nature, such that updating these models while keeping the compositional constraints is a practical requirement in order to improve the accuracy of the updated models. This paper presents an updating framework for compositional data based on ensemble Kalman filter which allows us to work with compositions that are transformed into a multivariate Gaussian space by log-ratio transformation and flow anamorphosis. This flow anamorphosis, transforms the distribution of the variables to joint normality while reasonably keeping the dependencies between components. Furthermore, the positiveness of those variables, after updating the simulated models, is satisfied. The method is implemented in a bauxite deposit, demonstrating the performance of the proposed approach.

     

Conditioning generative adversarial networks on nonlinear data for subsurface flow model calibration and uncertainty quantification

Conditioning complex subsurface flow models on nonlinear data is complicated by the need to preserve the expected geological connectivity patterns to maintain solution plausibility. Generative adversarial networks (GANs) have recently been proposed as a promising approach for low-dimensional representation of complex high-dimensional images. The method has also been adopted for low-rank parameterization of complex geologic models to facilitate uncertainty quantification workflows. A difficulty in adopting these methods for subsurface flow modeling is the complexity associated with nonlinear flow data conditioning. While conditional GAN (CGAN) can condition simulated images on labels, application to subsurface problems requires efficient conditioning workflows for nonlinear data, which is far more complex. We present two approaches for generating flow-conditioned models with complex spatial patterns using GAN. The first method is through conditional GAN, whereby a production response label is used as an auxiliary input during the training stage of GAN. The production label is derived from clustering of the flow responses of the prior model realizations (i.e., training data). The underlying assumption of this approach is that GAN can learn the association between the spatial features corresponding to the production responses within each cluster. An alternative method is to use a subset of samples from the training data that are within a certain distance from the observed flow responses and use them as training data within GAN to generate new model realizations. In this case, GAN is not required to learn the nonlinear relation between production responses and spatial patterns. Instead, it is tasked to learn the patterns in the selected realizations that provide a close match to the observed data. The conditional low-dimensional parameterization for complex geologic models with diverse spatial features (i.e., when multiple geologic scenarios are plausible) performed by GAN allows for exploring the spatial variability in the conditional realizations, which can be critical for decision-making. We present and discuss the important properties of GAN for data conditioning using several examples with increasing complexity.

     

三维矿床地质模型的不确定性

三维矿床地质模型的不确定性对矿山生产决策有着重要影响,正确地对矿床地质模型进行不确定性分析可以对其本身和在其基础上所做的决策作出科学评价。矿床地质模型的不确定性主要来自于建模数据和插值方法的不确定性。通过对建模数据的产生、处理过程的分析,利用处理不确定性问题的理论和方法建立建模数据的不确定性模型。通过对建模方法产生的理论误差和实测误差进行量化,实现对建模方法不确定性的定量描述。将建模数据的不确定性和建模方法的不确定性进行叠置分析,建立矿床模型的不确定性模型。以内蒙古自治区某煤矿的地质资料为例,通过不确定性分析,建立了该矿的不确定性三维矿床地质模型。      

Simulation of mineral grades with hard and soft conditioning data: application to a porphyry copper deposit

This work deals with the geostatistical simulation of mineral grades whose distribution exhibits spatial trends within the ore deposit. It is suggested that these trends can be reproduced by using a stationary random field model and by conditioning the realizations to data that incorporate the available information on the local grade distribution. These can be hard data (e.g., assays on samples) or soft data (e.g., rock-type information) that account for expert geological knowledge and supply the lack of hard data in scarcely sampled areas. Two algorithms are proposed, depending on the kind of soft data under consideration: interval constraints or local moment constraints. An application to a porphyry copper deposit is presented, in which it is shown that the incorporation of soft conditioning data associated with the prevailing rock type improves the modeling of the uncertainty in the actual copper grades.     

Modeling Combined Geological and Grade Uncertainty: Application of Multiple-Point Simulation at the Apensu Gold Deposit, Ghana

Traditionally within the mining industry, single models for both grade and geology of orebodies are created upon which all mine development decisions are based. These models provide a single interpretation of the extent and continuity of the mineralization envelope based on solids and sections interpreted from relatively widely spaced drilling. The inherent variable behavior of grade and geology cannot be understood from a single estimated resource model. To account for uncertainty in the geology and mineralization envelope, Newmont Mining Corporation uses multiple-point statistics (MPS), an emerging spatial simulation framework, which can be employed to generate multiple, geologically realistic, realizations of data representing attributes of mineral deposits that display complex non-linear features. MPS uses a conceptual model of the geology, termed a training image, to infer these high-order spatial relationships. A detailed application of the MPS algorithm at the structurally controlled Apensu gold deposit, Ghana, demonstrates the practical intricacies of the MPS framework and documents efficiency and effectiveness. Multiple realizations of the Apensu deposit allow for an assessment of the geologic and volumetric uncertainty, which is further combined with grade simulations to generate a more complete picture of the true uncertainty of the deposit.     

Risk quantification with combined use of lithological and grade simulations: Application to a porphyry copper deposit

The uncertainty in the recoverable tonnages and grades in a mineral deposit is a key factor in the decision-making process of a mining project. Currently, the most prevalent approach to model the uncertainty in the spatial distribution of mineral grades is to divide the deposit into domains based on geological interpretation and to predict the grades within each domain separately. This approach defines just one interpretation of the geological domain layout and does not offer any measure of the uncertainty in the position of the domain boundaries and in the mineral grades. This uncertainty can be evaluated by use of geostatistical simulation methods. The aim of this study is to evaluate how the simulation of rock type domains and grades affects the resources model of Sungun porphyry copper deposit, northwestern Iran. Specifically, three main rock type domains (porphyry, skarn and late-injected dykes) that control the copper grade distribution are simulated over the region of interest using the plurigaussian model. The copper grades are then simulated in cascade, generating one grade realization for each rock type realization. The simulated grades are finally compared to those obtained using traditional approaches against production data.     

Conditioning of Multiple-Point Statistics Facies Simulations to Tomographic Images

Geophysical tomography captures the spatial distribution of the underlying geophysical property at a relatively high resolution, but the tomographic images tend to be blurred representations of reality and generally fail to reproduce sharp interfaces. Such models may cause significant bias when taken as a basis for predictive flow and transport modeling and are unsuitable for uncertainty assessment. We present a methodology in which tomograms are used to condition multiple-point statistics (MPS) simulations. A large set of geologically reasonable facies realizations and their corresponding synthetically calculated cross-hole radar tomograms are used as a training image. The training image is scanned with a direct sampling algorithm for patterns in the conditioning tomogram, while accounting for the spatially varying resolution of the tomograms. In a post-processing step, only those conditional simulations that predicted the radar traveltimes within the expected data error levels are accepted. The methodology is demonstrated on a two-facies example featuring channels and an aquifer analog of alluvial sedimentary structures with five facies. For both cases, MPS simulations exhibit the sharp interfaces and the geological patterns found in the training image. Compared to unconditioned MPS simulations, the uncertainty in transport predictions is markedly decreased for simulations conditioned to tomograms. As an improvement to other approaches relying on classical smoothness-constrained geophysical tomography, the proposed method allows for: (1) reproduction of sharp interfaces, (2) incorporation of realistic geological constraints and (3) generation of multiple realizations that enables uncertainty assessment.     

Simulation of Geological Contacts from Interpreted Geological Model Using Multiple-Point Statistics

Applications of multiple-point statistics (mps) algorithms to large non-repetitive geological objects such as those found in mining deposits are difficult because most mps algorithms rely on pattern repetition for simulation. In many cases, an interpreted geological model built from a computer-aided design system is readily available but suffers as a training image due to the lack of patterns repetitiveness. Porphyry copper deposits and iron ore formations are good examples of such mining deposits with non-repetitive patterns. This paper presents an algorithm called contactsim that focuses on reproducing the patterns of the contacts between geological types. The algorithm learns the shapes of the lithotype contacts as interpreted by the geologist, and simulates their patterns at a later stage. Defining a zone of uncertainty around the lithological contact is a critical step in contactsim, because it defines both the zones where the simulation is performed and where the algorithm should focus to learn the transitional patterns between lithotypes. A larger zone of uncertainty results in greater variation between realizations. The definition of the uncertainty zone must take into consideration the geological understanding of the deposit, and the reliability of the contact zones. The contactsim algorithm is demonstrated on an iron ore formation.     

三维成矿预测数据整合过程不确定性研究——以宁芜盆地钟姑矿田为例

基于多元地学大数据的三维成矿预测方法是开展深部找矿预测的新方法和新手段,也是当前成矿预测领域的研究热点之一。然而,大数据具有高维、混杂、非精确等特点,其分析处理过程面临多重不确定性。多元地学大数据整合是三维成矿预测的最终环节,其存在的不确定性将直接作用于预测结果,影响进一步的找矿应用和风险评估。本文以宁芜盆地钟姑矿田为例,从大数据思维出发,定量分析和度量预测要素和数学模型在数据整合过程中存在的不确定性及对三维成矿预测结果的影响。结果显示,断裂构造、背斜轴部等预测要素的不确定性对三维成矿预测结果的影响最为强烈;数据整合模型中,较之Logistic回归模型和证据权重模型,神经网络模型可能具有更高的不确定性程度。进一步工作可通过增强上述预测要素的可靠性和有效性、采用更多的数据整合模型进行更为全面的不确定性分析和评价,以获得更为可靠的三维成矿预测成果,从而降低成矿预测和找矿勘探风险。     

河南栾川西沟铅锌银金矿床三维地质建模与深部找矿预测评价

随着矿区浅部矿的日益减少,深部找矿越来越受到重视,三维地质建模技术在成矿预测、资源定量评价等方面得到了广泛的应用.本文利用三维地质建模平台GOCAD中的三维建模技术及地质统计学等方法,基于收集测试得到的地质图、钻孔和采样点的地层、岩性、构造、品位等数据,构建了西沟铅锌银金矿区的三维地质模型,包括断裂构造模型、矿体模型及...     

试论固体矿产普查、勘探与开发的合理程序

<正> 固体矿产普查勘探与开发程序,不仅是当前地质勘探和矿山建设工作中的实际问题,也是国内外学者和矿业学家多年来不断进行探讨和研究的一项理论课题。 苏联和东欧一些国家矿业活动实行国家管理,对地质普查、勘探程序一向极为重视。长期以来,他们通过制定各类矿产的勘探方法和储量规范,或由政府颁布有关条例、规程等形式对阶段程序作出统一规定,要求统一贯彻执行。     

Integration of Markov mesh models and data assimilation techniques in complex reservoirs

We present a methodology that allows conditioning the spatial distribution of geological and petrophysical properties of reservoir model realizations on available production data. The approach is fully consistent with modern concepts depicting natural reservoirs as composite media where the distribution of both lithological units (or facies) and associated attributes are modeled as stochastic processes of space. We represent the uncertain spatial distribution of the facies through a Markov mesh (MM) model, which allows describing complex and detailed facies geometries in a rigorous Bayesian framework. The latter is then embedded within a history matching workflow based on an iterative form of the ensemble Kalman filter (EnKF). We test the proposed methodology by way of a synthetic study characterized by the presence of two distinct facies. We analyze the accuracy and computational efficiency of our algorithm and its ability with respect to the standard EnKF to properly estimate model parameters and assess future reservoir production. We show the feasibility of integrating MM in a data assimilation scheme. Our methodology is conducive to a set of updated model realizations characterized by a realistic spatial distribution of facies and their log permeabilities. Model realizations updated through our proposed algorithm correctly capture the production dynamics.     

Markov chain Monte Carlo methods for conditioning a permeability field to pressure data

Generating one realization of a random permeability field that is consistent with observed pressure data and a known variogram model is not a difficult problem. If, however, one wants to investigate the uncertainty of reservior behavior, one must generate a large number of realizations and ensure that the distribution of realizations properly reflects the uncertainty in reservoir properties. The most widely used method for conditioning permeability fields to production data has been the method of simulated annealing, in which practitioners attempt to minimize the difference between the ’ ’true and simulated production data, and “true” and simulated variograms. Unfortunately, the meaning of the resulting realization is not clear and the method can be extremely slow. In this paper, we present an alternative approach to generating realizations that are conditional to pressure data, focusing on the distribution of realizations and on the efficiency of the method. Under certain conditions that can be verified easily, the Markov chain Monte Carlo method is known to produce states whose frequencies of appearance correspond to a given probability distribution, so we use this method to generate the realizations. To make the method more efficient, we perturb the states in such a way that the variogram is satisfied automatically and the pressure data are approximately matched at every step. These perturbations make use of sensitivity coefficients calculated from the reservoir simulator.     

三维地质模拟在深部找矿勘探中的应用

我国矿产资源形势严峻,使深部找矿勘探工作的重要性大大提高。三维地质模拟作为一种新型有效技术,利用立体建模的方式建立矿床三维模型,可定量定位地表达各种地质信息,有效地恢复矿区的深部与浅部的构造形态,这些地质信息共同存在于相同的三维空间中,受钻孔等直接信息数据的约束,更接近现实世界。本文论述了三维地质模拟在深部找矿工作中的广泛应用,包括深部矿床等地质体建模、综合分析、多种图件的自动绘制等,可为矿床储量估算、成矿规律总结、深部成矿预测和矿山生产等工作提供直观、快速的数据和技术支持。     

3D矿床建模技术在数字矿产勘查中的应用

为弥补现有数字矿床建模技术在地质矿产勘查处理和应用中的不足,从原始勘查数据建库及标准化、多指标单工程矿体自动圈定、基于语义识别的剖面矿体的连接与外推、矿体表面和品位建模、基于剖面矿体线框模型构建矿体表面模型及基于TIN+Octree数据结构和地质统计学理论建立矿体的空间属性模型等5个方面总结提出一套面向地质矿产勘查业务处理的矿床建模流程和总体技术解决方案.提高了地质矿产勘查研究精度,为进一步的矿山开采提供可靠的数据模型.      

A multi-resolution workflow to generate high-resolution models constrained to dynamic data

Distance-based stochastic techniques have recently emerged in the context of ensemble modeling, in particular for history matching, model selection and uncertainty quantification. Starting with an initial ensemble of realizations, a distance between any two models is defined. This distance is defined such that the objective of the study is incorporated into the geological modeling process, thereby potentially enhancing the efficacy of the overall workflow. If the intent is to create new models that are constrained to dynamic data (history matching), the calculation of the distance requires flow simulation for each model in the initial ensemble. This can be very time consuming, especially for high-resolution models. In this paper, we present a multi-resolution framework for ensemble modeling. A distance-based procedure is employed, with emphasis on the rapid construction of multiple models that have improved dynamic data conditioning. Our intent is to construct new high-resolution models constrained to dynamic data, while performing most of the flow simulations only on upscaled models. An error modeling procedure is introduced into the distance calculations to account for potential errors in the upscaling. Based on a few fine-scale flow simulations, the upscaling error is estimated for each model using a clustering technique. We demonstrate the efficiency of the method on two examples, one where the upscaling error is small, and another where the upscaling error is significant. Results show that the error modeling procedure can accurately capture the error in upscaling, and can thus reproduce the fine-scale flow behavior from coarse-scale simulations with sufficient accuracy (in terms of uncertainty predictions). As a consequence, an ensemble of high-resolution models, which are constrained to dynamic data, can be obtained, but with a minimum of flow simulations at the fine scale.     

A flow-based pattern recognition algorithm for rapid quantification of geologic uncertainty

Geologic uncertainties and limited well data often render recovery forecasting a difficult undertaking in typical appraisal and early development settings. Recent advances in geologic modeling algorithms permit automation of the model generation process via macros and geostatistical tools. This allows rapid construction of multiple alternative geologic realizations. Despite the advances in geologic modeling, computation of the reservoir dynamic response via full-physics reservoir simulation remains a computationally expensive task. Therefore, only a few of the many probable realizations are simulated in practice. Experimental design techniques typically focus on a few discrete geologic realizations as they are inherently more suitable for continuous engineering parameters and can only crudely approximate the impact of geology. A flow-based pattern recognition algorithm (FPRA) has been developed for quantifying the forecast uncertainty as an alternative. The proposed algorithm relies on the rapid characterization of the geologic uncertainty space represented by an ensemble of sufficiently diverse static model realizations. FPRA characterizes the geologic uncertainty space by calculating connectivity distances, which quantify how different each individual realization is from all others in terms of recovery response. Fast streamline simulations are employed in evaluating these distances. By applying pattern recognition techniques to connectivity distances, a few representative realizations are identified within the model ensemble for full-physics simulation. In turn, the recovery factor probability distribution is derived from these intelligently selected simulation runs. Here, FPRA is tested on an example case where the objective is to accurately compute the recovery factor statistics as a function of geologic uncertainty in a channelized turbidite reservoir. Recovery factor cumulative distribution functions computed by FPRA compare well to the one computed via exhaustive full-physics simulations.