Well Conditioning in a Fluvial Reservoir Model

This paper describes a method for conditioning an object model of a fluvial reservoir on facies observations. The channels are assumed parametrized at sections normal to their main channel direction. Projections of the observations on these sections generates a map suitable for drawing conditioning values. This map contains the information from every facies observation between two adjacent sections, enabling handling of any well path. Coupling between well observations is also discussed. The methodology is implemented and demonstrated in examples with complex wells.     

Improving Sequential Simulation with a Structured Path Guided by Information Content

Multiple-point simulation is a newly developed geostatistical method that aims at combining the strengths of two mainstream geostatistical methods: object-based and pixel-based methods. It maintains the flexibility of pixel-based algorithms in data conditioning, while enhancing its capability of reproducing realistic geological shapes, which is traditionally reserved to object-based algorithms. However, the current snesim program for multiple-point simulation has difficulty in reproducing large-scale structures, which have a significant impact on the flow response. To address this problem, we propose to simulate along a structured path based on an information content measure. This structured path accounts for not only the information from the data, but also some prior structural information provided by geological knowledge. Various case studies show a better reproduction of large-scale structures. This concept of simulating along a structured path guided by information content can be applied to any sequential simulation algorithms, including traditional variogram-based two-point geostatistical algorithms.     

Spectral Simulation and Conditioning to Local Continuity Trends in Geologic Modeling

Spectral simulation has gained application in building geologic models due to the advantage of better honoring the spatial continuity of petrophysical properties, such as reservoir porosity and shale volume. Distinct from sequential simulation methods, spectral simulation is a global algorithm in the sense that a global density spectrum is calculated once and the inverse Fourier transform is performed on the Fourier coefficient also only once to generate a simulation realization. The generated realizations honor the spatial continuity structure globally over the whole field instead of only within a search neighborhood, as with sequential simulation algorithms. However, the disadvantage of global spectral simulation is that it traditionally cannot account for the local information such as the local continuity trends, which are often observed in reservoirs and hence are important to be accounted for in geologic models. This disadvantage has limited wider application of spectral simulation in building geologic models. In this paper, we present ways of conditioning geologic models to the relevant local information. To account for the local continuity trends, we first scale different frequency components of the original model with local-amplitude spectrum ratios that are specific to the local trend. The sum of these scaled frequency components renders a new model that displays the desired local continuity trend. The implementation details of this new method are discussed and examples are provided to illustrate the algorithm.     

Two Artifacts of Probability Field Simulation

Probability field simulation is being used increasingly to simulate geostatistical realizations. The method can be faster than conventional simulation algorithms and it is well suited to integrate prior soft information in the form of local probability distributions. The theoretical basis of probability field simulation has been established when there are no conditioning data; however, no such basis has been established in presence of conditioning data. Realizations generated by probability field simulation show two severe artifacts near conditioning data. We document these artifacts and show theoretically why they exist. The two artifacts that have been investigated are (1) local conditioning data appear as local minima or maxima of the simulated values, and (2) the variogram model in range of conditioning data is not honored; the simulated values have significantly greater continuity than they are supposed to. These two artifacts are predicted by theory. An example flow simulation study is presented to illustrate that they affect more than the visual appearance of the simulated realizations. Notwithstanding the flexibility of the probability field simulation method, these two artifacts suggest that it be used with caution in presence of conditioning data. Future research may overcome these limitations.     

多点地质统计学：理论、应用与展望

本文系统地介绍了多点地质统计学的基本原理及方法，并以我国渤海湾盆地某区块新近系明化镇组河流相储层为例，进行了多点统计学随机建模的实例分析。多点地质统计学为储层随机建模的国际前沿研究方向，该方法综合了基于象元的方法易忠实条件数据以及基于目标的方法易再现目标几何形态的优点，同时克服了传统基于变差函数的二点统计学不能表达复杂空间结构和再现目标几何形态的不足。通过理论与实例研究，分析了目前多点统计学尚存在的问题(包括训练图像平稳性问题、目标连续性问题以及综合软信息的问题等)及未来发展的方向。     

ODSIM: An Object-Distance Simulation Method for Conditioning Complex Natural Structures

Stochastic simulation of categorical objects is traditionally achieved either with object-based or pixel-based methods. Whereas object-based modeling provides realistic results but raises data conditioning problems, pixel-based modeling provides exact data conditioning but may lose some features of the simulated objects such as connectivity. We suggest a hybrid dual-scale approach to combine both shape realism and strict data conditioning. The procedure combines the distance transform to a skeleton object representing coarse-scale structures, plus a classical pixel-based random field and threshold representing fine-scale features. This object-distance simulation method (ODSIM) uses a perturbed distance to objects and is particularly appropriate for modeling structures related to faults or fractures such as karsts, late dolomitized rocks, and mineralized veins. We demonstrate this method to simulate dolomite geometry and discuss strategies to apply this method more generally to simulate binary shapes.     

基于改进三棱柱模型的复杂地质体3D建模方法

建模方法是三维地质模型及其可视化研究的核心内容。针对连续体终止、错断位移等复杂地质体3D地质建摸的需要，本文对现有的三棱柱数据模型进行了改进，构建了完整的数据结构及其初步的拓扑关系，提出了基于改进三棱柱模型的连续体和不连续体的建摸算法，使其在处理地层尖灭、断层等复杂地质问题时更为灵活、适应面更广。     

Theoretical connections between optimization algorithms based on an approximate gradient

Performing a line search method in the direction given by the simplex gradient is a well-known method in the mathematical optimization community. For reservoir engineering optimization problems, both a modification of the simultaneous perturbation stochastic approximation (SPSA) and ensemble-based optimization (EnOpt) have recently been applied for estimating optimal well controls in the production optimization step of closed-loop reservoir management. The modified SPSA algorithm has also been applied to assisted history-matching problems. A recent comparison of the performance of EnOpt and a SPSA-type algorithm (G-SPSA) for a set of production optimization test problems showed that the two algorithms resulted in similar estimates of the optimal net-present-value and required roughly the same amount of computational time to achieve these estimates. Here, we show that, theoretically, this result is not surprising. In fact, we show that both the simplex, preconditioned simplex, and EnOpt algorithms can be derived directly from a modified SPSA-type algorithm where the preconditioned simplex algorithm is presented for the first time in this paper. We also show that the expectation of all these preconditioned stochastic gradients is a first-order approximation of the preconditioning covariance matrix times the true gradient or a covariance matrix squared times the true gradient.     

Automatic Identification of Rock Fracture Sets Using Finite Mixture Models

The clustering and classification of fracture orientation data are crucial tasks in geotechnical engineering and rock engineering design. The explicit simulation of fracture orientations is always applied to compensate for the lack of direct measurements over the entire rock mass. In this study, a single step approach based on the theory of finite mixture models, where the component distributions are Fisher distributions, is proposed for automatic clustering and simulation of fracture orientation data. In the proposed workflow, the spherical K-means algorithm is applied to select the initial cluster centers, and the component-wise expectation–maximization algorithm using the minimum message length criterion is used to automatically determine the optimal number of fracture sets. An additional advantage of the proposed method is the representation of orientation data using a full sphere, instead of the conventional hemispherical characterization. The use of a full spherical representation effectively solves the issue of clustering for fractures with high dip angles. In addition, the calculation process of the mean direction is also simplified. The effectiveness of the model-based clustering method is tested with a complicated artificial data set and two real world data sets. Cluster validity is introduced to evaluate the clustering results. In addition, two other clustering algorithms are also presented for comparison. The results demonstrate that the proposed method can successfully detect the optimal number of clusters, and the parameters of the distributions are well estimated. In addition, the proposed method also exhibits good computational performance.     

A fast intensity simulator for tropical cyclone risk analysis

Robust estimates of tropical cyclone risk can be made using large sets of storm events synthesized from historical data or from physics-based algorithms. While storm tracks can be synthesized very rapidly from statistical algorithms or simple dynamical models (such as the beta-and-advection model), estimation of storm intensity by using full-physics models is generally too expensive to be practical. Although purely statistical intensity algorithms are fast, they may not be general enough to encompass the effects of natural or anthropogenic climate change. Here we present a fast, physically motivated intensity algorithm consisting of two coupled ordinary differential equations predicting the evolution of a wind speed and an inner core moisture variable. The algorithm includes the effects of ocean coupling and environmental wind shear but does not explicitly simulate spatial structure, which must be handled parametrically. We evaluate this algorithm by using it to simulate several historical events and by comparing a risk analysis based on it to an existing method for assessing long-term tropical cyclone risk. For simulations based on the recent climate, the two techniques perform comparably well, though the new technique does better with interannual variability in the Atlantic. Compared to the existing method, the new method produces a smaller increase in global tropical cyclone frequency in response to global warming, but a comparable increase in power dissipation.     

地下水空调技术与应用

本文以季节性的舒适性空调为对象，较详细地介绍了地下水人调供冷的基本原理，特点、供冷负荷的计算方法，地下水风机盘管空调系统的布置、测试与维护管理，实用效果以及地下水空调技术的应用前景。     

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.

     

Explicit stress integration with error control for the Barcelona Basic Model.: Part II: Algorithms efficiency and accuracy

The paper compares the accuracy and efficiency of explicit stress integration schemes for elasto-plastic unsaturated soil models with automatic error control. Numerical tests are performed with reference to the Barcelona Basic Model (BBM), one of the most popular elasto-plastic models for unsaturated soils, by using eight explicit Runge–Kutta algorithms of various order as well as a novel application of the extrapolation method described in the companion paper. Initially, the results obtained from the lowest order Runge–Kutta scheme (i.e. Modified Euler) as well as the extrapolation method are checked against accurate solutions of a number of BBM paths involving changes of strains and suction. Subsequently, the efficiency and accuracy of all algorithms are assessed for generic increments of strains and suction, while the difference between two alternative error control methods is also analysed. The results presented, although strictly valid for the Barcelona Basic Model, are expected to be general and relevant to other similar unsaturated elasto-plastic models formulated in terms of two independent stress variables such as net stress and suction.     

Multiple-Point Simulation with an Existing Reservoir Model as Training Image

The multiple-point simulation (MPS) method has been increasingly used to describe the complex geologic features of petroleum reservoirs. The MPS method is based on multiple-point statistics from training images that represent geologic patterns of the reservoir heterogeneity. The traditional MPS algorithm, however, requires the training images to be stationary in space, although the spatial distribution of geologic patterns/features is usually nonstationary. Building geologically realistic but statistically stationary training images is somehow contradictory for reservoir modelers. In recent research on MPS, the concept of a training image has been widely extended. The MPS approach is no longer restricted by the size or the stationarity of training images; a training image can be a small geometrical element or a full-field reservoir model. In this paper, the different types of training images and their corresponding MPS algorithms are first reviewed. Then focus is placed on a case where a reservoir model exists, but needs to be conditioned to well data. The existing model can be built by process-based, object-based, or any other type of reservoir modeling approach. In general, the geologic patterns in a reservoir model are constrained by depositional environment, seismic data, or other trend maps. Thus, they are nonstationary, in the sense that they are location dependent. A new MPS algorithm is proposed that can use any existing model as training image and condition it to well data. In particular, this algorithm is a practical solution for conditioning geologic-process-based reservoir models to well data.     

Adaptive Conditioning of Multiple-Point Statistical Facies Simulation to Flow Data with Probability Maps

Multiple-point statistics (MPS) provides a flexible grid-based approach for simulating complex geologic patterns that contain high-order statistical information represented by a conceptual prior geologic model known as a training image (TI). While MPS is quite powerful for describing complex geologic facies connectivity, conditioning the simulation results on flow measurements that have a nonlinear and complex relation with the facies distribution is quite challenging. Here, an adaptive flow-conditioning method is proposed that uses a flow-data feedback mechanism to simulate facies models from a prior TI. The adaptive conditioning is implemented as a stochastic optimization algorithm that involves an initial exploration stage to find the promising regions of the search space, followed by a more focused search of the identified regions in the second stage. To guide the search strategy, a facies probability map that summarizes the common features of the accepted models in previous iterations is constructed to provide conditioning information about facies occurrence in each grid block. The constructed facies probability map is then incorporated as soft data into the single normal equation simulation (snesim) algorithm to generate a new candidate solution for the next iteration. As the optimization iterations progress, the initial facies probability map is gradually updated using the most recently accepted iterate. This conditioning process can be interpreted as a stochastic optimization algorithm with memory where the new models are proposed based on the history of the successful past iterations. The application of this adaptive conditioning approach is extended to the case where multiple training images are proposed as alternative geologic scenarios. The advantages and limitations of the proposed adaptive conditioning scheme are discussed and numerical experiments from fluvial channel formations are used to compare its performance with non-adaptive conditioning techniques.     

GANSim: Conditional Facies Simulation Using an Improved Progressive Growing of Generative Adversarial Networks (GANs)

Conditional facies modeling combines geological spatial patterns with different types of observed data, to build earth models for predictions of subsurface resources. Recently, researchers have used generative adversarial networks (GANs) for conditional facies modeling, where an unconditional GAN is first trained to learn the geological patterns using the original GAN’s loss function, then appropriate latent vectors are searched to generate facies models that are consistent with the observed conditioning data. A problem with this approach is that the time-consuming search process needs to be conducted for every new conditioning data. As an alternative, we improve GANs for conditional facies simulation (called GANSim) by introducing an extra condition-based loss function and adjusting the architecture of the generator to take the conditioning data as inputs, based on progressive growing of GANs. The condition-based loss function is defined as the inconsistency between the input conditioning value and the corresponding characteristics exhibited by the output facies model, and forces the generator to learn the ability of being consistent with the input conditioning data, together with the learning of geological patterns. Our input conditioning factors include global features (e.g., the mud facies proportion) alone, local features such as sparse well facies data alone, and joint combination of global features and well facies data. After training, we evaluate both the quality of generated facies models and the conditioning ability of the generators, by manual inspection and quantitative assessment. The trained generators are quite robust in generating high-quality facies models conditioned to various types of input conditioning information.

     

Landslide Susceptibility Mapping Using GIS-based Fuzzy Logic and the Analytical Hierarchical Processes Approach: A Case Study in Constantine (North-East Algeria)

The main purpose of this study was to compare and evaluate the performance of two multicriteria models for landslide susceptibility assessment in Constantine, north-east of Algeria. The landslide susceptibility maps were produced using the analytic hierarchy process (AHP) and Fuzzy AHP (FAHP) via twelve landslides conditioning factors, including the slope gradient, lithology, land cover, distance from drainage network, distance from the roads, distance from faults, topographic wetness index, stream power index, slope curvature, Normalized Difference Vegetation Index, slope aspect and elevation. In this study, the mentioned models were used to derive the weighting value of the conditioning factors. For the validation process of these models, the receiver operating characteristic analysis, and the area under the curve (AUC) were applied by comparing the obtained results to The landslide inventory map which prepared using the archives of scientific publications, reports of local authorities, and field survey as well as analyzing satellite imagery. According to the AUC values, the FAHP model had the highest value (0.908) followed by the AHP model (0.777). As a result, the FAHP model is more consistent and accurate than the AHP in this case study. The outcome of this paper may be useful for landslide susceptibility assessment and land use management.

     

Spatial prediction models for shallow landslide hazards: a comparative assessment of the efficacy of support vector machines,artificial neural networks,kernel logistic regression,and logistic model tree

Preparation of landslide susceptibility maps is considered as the first important step in landslide risk assessments, but these maps are accepted as an end product that can be used for land use planning. The main objective of this study is to explore some new state-of-the-art sophisticated machine learning techniques and introduce a framework for training and validation of shallow landslide susceptibility models by using the latest statistical methods. The Son La hydropower basin (Vietnam) was selected as a case study. First, a landslide inventory map was constructed using the historical landslide locations from two national projects in Vietnam. A total of 12 landslide conditioning factors were then constructed from various data sources. Landslide locations were randomly split into a ratio of 70:30 for training and validating the models. To choose the best subset of conditioning factors, predictive ability of the factors were assessed using the Information Gain Ratio with 10-fold cross-validation technique. Factors with null predictive ability were removed to optimize the models. Subsequently, five landslide models were built using support vector machines (SVM), multi-layer perceptron neural networks (MLP Neural Nets), radial basis function neural networks (RBF Neural Nets), kernel logistic regression (KLR), and logistic model trees (LMT). The resulting models were validated and compared using the receive operating characteristic (ROC), Kappa index, and several statistical evaluation measures. Additionally, Friedman and Wilcoxon signed-rank tests were applied to confirm significant statistical differences among the five machine learning models employed in this study. Overall, the MLP Neural Nets model has the highest prediction capability (90.2 %), followed by the SVM model (88.7 %) and the KLR model (87.9 %), the RBF Neural Nets model (87.1 %), and the LMT model (86.1 %). Results revealed that both the KLR and the LMT models showed promising methods for shallow landslide susceptibility mapping. The result from this study demonstrates the benefit of selecting the optimal machine learning techniques with proper conditioning selection method in shallow landslide susceptibility mapping.     

Fast Web - Based Data Transmission

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A Stochastic Object Model Conditioned to High-Quality Seismic Data

We present an approach for modeling facies bodies in which a highly constrained stochastic object model is used to integrate detailed seismic interpretation of the reservoir’s sedimentological architecture directly in a three-dimensional reservoir model. The approach fills the gap between the use of seismic data in a true deterministic sense, in which the facies body top and base are resolved and mapped directly, and stochastic methods in which the relationship between seismic attributes and facies is defined by conditional probabilities. The lateral geometry of the facies bodies is controlled by seismic interpretations on horizon slices or by direct body extraction, whereas facies body thickness and cross-sectional shape are defined by a mixture of seismic data, well data, and user defined object shapes. The stochastic terms in the model are used to incorporate local geometric variability, which is used to increase the geological realism of the facies bodies and allow for correct, flexible well conditioning. The result is a set of three-dimensional facies bodies that are constrained to the seismic interpretations and well data. Each body is defined as a parametric object that includes information such as location of the body axis, depositional direction, axis-to-margin normals, and external body geometry. The parametric information is useful for defining geologically realistic intrabody petrophysical trends and for controlling connectivity between stacked facies bodies.