An adaptive grid technique for minimizing heterogeneity of cells or elements

Geostatistical techniques allow simulation of properties such as porosity or conductivity on a fine scale. Typically, porous media flow modeling is performed at a coarser scale. Upscaling properties from the fine scale to the coarser scale introduces potential errors which are constrained by the degree of homogeneity of the cell or element. Adaptive grid techniques can be used to minimize the heterogeneity in the individual cells or elements, thus minimizing potential upscaling errors. A geostatistical adaptive grid (GAG) algorithm based on local minimization of heterogeneity is introduced. Local minimization allows greater control over the type of distortion permitted. Comparisons are made with a general elastic grid adjustment (GEGA) algorithm based on global minimization of heterogeneity. Several sample problems are used to test and demonstrate the two approaches.     

Spatial grid correction for short-term numerical simulation results of carbon dioxide dissolution in saline aquifers

Numerical simulation is an essential component of many studies of geological storage of carbon dioxide, but care must be taken to ensure the accuracy of the results. Unlike several other possible sources of simulation errors, which have previously been considered in detail and have well-understood techniques for mitigating their effects, comparatively little discussion of the spatial grid dependence of the dissolution rate of carbon dioxide into the formation water has appeared in the literature, despite its importance to simulation studies of geological storage of carbon dioxide in saline aquifers. In many instances, sufficient refinement of the computational grid can be a practical solution. However, this approach is not always feasible, especially for large-scale simulations in three dimensions requiring multiple realisations, which commonly feature a coarse grid due to constraints on available computational capabilities. A measure of the error in the amount of dissolved carbon dioxide introduced by the use of a finite grid is therefore of great interest. In this study, the use of finite-sized grid blocks is shown to overestimate the amount of dissolved carbon dioxide in short-term results by a factor of 1?+?V _f/V _p, where V _f is the grid block volume at the saturation front and V _p is the total grid block volume of the plume. This result can be used in a number of ways to correct the calculated short-term dissolution in coarse-scale simulations so that the amount dissolved agrees better with that obtained from fine-scale simulations.     

Isotherms for the sorption of zinc and copper onto kaolinite: comparison of various error functions

In this research, the equilibrium sorption of Zn(II) and Cu(II) by kaolinite was explained using the Freundlich, Langmuir and Redlich–Peterson isotherms, via both linear and non-linear regression analyses. In the case of non-linear regression method, the best-fitting model was evaluated using six different error functions, namely coefficient of determination (r ²), hybrid fractional error function (HYBRID), Marquardt’s percent standard deviation (MPSD), average relative error (ARE), sum of the errors squared (SSE) and sum of the absolute errors (EABS). The examination of error estimation methods showed that the Langmuir model provides the best fit for the experimental equilibrium data for both linear and non-linear regression analyses. The SSE function was found to be a better option to minimize the error distribution between the experimental equilibrium data and predicted two-parameter isotherms. In the case of three-parameter isotherm, HYBRID was found to be the best error function to minimize the error distribution structure between experimental equilibrium data and theoretical isotherms. Non-linear method was found to be more appropriate method for estimating the isotherm parameters.     

A computer simulation study of natural silicate melts. Part I: Low pressure properties

In implementing into a molecular dynamics simulation code a simple interionic potential developed to describe the nine component system K₂O-Na₂O-CaO-MgO-FeO-Fe₂O₃-Al₂O₃-TiO₂-SiO₂ (KNCMFATS), it has been possible to reproduce satisfactorily a number of thermodynamic, structural and transport properties of a representative set of natural silicate melts. An important conclusion reached in this study is the good transferability of the potential from felsic to ultramafic compositions although this transferability becomes less accurate with high silica contents (rhyolitic composition and beyond) and with very iron-rich silicates (e.g. fayalite). A key feature of the simulation is to make the link between macroscopic properties of the melt and its microscopic structure and dynamics. We thus obtain a relationship between the molar volume of the melt, the number of network modifiers and the oxygen coordination number. The simulation also allows one to quantify the coordination environment around the cations as function of the melt composition. Furthermore, the electrical conductivity of the high temperature liquid is investigated.     

New algorithms in 3D image analysis and their application to the measurement of a spatialized pore size distribution in soils

We introduce a skeletization method based on the Voronoi diagram to determine local pore sizes in any porous medium. Using the skeleton of the pore space in a 3D image of the porous medium, a pore size value is assigned to each voxel and a reconstructed image of a spatialized local pore size distribution is created. The reconstructed image provides a means for calculating the global volume versus size pore distribution. It is also used to carry out fluid invasion simulation which take into account the connectivity of and constrictions in the pore network. As an example we simulate mercury intrusion in a 3D soil image.     

Assessing the performance of a foraminifera-based transfer function to estimate sea-level changes in northern Portugal

We assessed the performance of a transfer function model for sea-level studies using salt-marsh foraminifera from two estuaries of northern Portugal. An independent data set of 12 samples and 13 sub-fossil samples from a core were used to evaluate if reconstructions and errors derived from current models are adequate. Initial transfer function models provided very strong results as indicated by cross-validation (component 2; r² = 0.80-0.82; RMSEP ranged from 10.7 to 12.3 cm) and improved its performance by ca. 10% when sample size reached ca. 50. Results derived using an independent test data set indicate that cross-validation is a very effective approach and produces conservative errors when compared to observed errors. We additionally explored the possible effect of transforming the concentration data into percent in the error estimations by comparing the results obtained based on the use of both concentration and compositional data. Results indicate that this type of transformation does not affect the performance of the transfer function. Results derived from a reconstruction of sub-fossil samples from a core indicate that high-resolution sea-level reconstructions are possible, but show that depositional environments have to be selected carefully in order to minimize the impact of possible taphonomical loss.     

Interior boundary-aligned unstructured grid generation and cell-centered versus vertex-centered CVD-MPFA performance

Grid generation for reservoir simulation must honor classical key constraints and be boundary aligned such that control-volume boundaries are aligned with geological features such as layers, shale barriers, fractures, faults, pinch-outs, and multilateral wells. An unstructured grid generation procedure is proposed that automates control-volume and/or control point boundary alignment and yields a PEBI-mesh both with respect to primal and dual (essentially PEBI) cells. In order to honor geological features in the primal configuration, we introduce the idea of protection circles, and to generate a dual-cell feature based grid, we construct halos around key geological features. The grids generated are employed to study comparative performance of cell-centred versus cell-vertex control-volume distributed multi-point flux approximation (CVD-MPFA) finite-volume formulations using equivalent degrees of freedom. The formulation of CVD-MPFA schemes in cell-centred and cell-vertex modes is analogous and requires switching control volume from primal to dual or vice versa together with appropriate data structures and boundary conditions. The relative benefits of both types of approximation, i.e., cell-centred versus vertex-centred, are made clear in terms of flow resolution and degrees of freedom required.     

Generalized sequential kriging (GSK) for heterogeneous cell size: property modeling without matrices

Sequential kriging avoids the use of matrices and resolves the issue of unstable solutions. It allows for stepwise ways to get joint estimations and cosimulations that are equivalent to the simultaneous solution. The approach is proposed as the solution for geocellular modeling with variable cell size from heterogeneous structural properties (HSPs) as required for modeling with structural constraints. Rock properties are controlled by structural domains, regions, and structural geology parameters. In some cases, rock properties are cross-correlated to formation thickness, curvature of structures, and other structural attributes. Cell thickness may be proportional to formation thickness and may enter as a conditioning property in the estimation of rock property parameters for simulation. In addition, cell volume controls the upscaling of covariance structures (i.e., regularized variograms). Structural properties are priorly modeled. Perturbation response functions (PRFs) are computed for each cell vs all possible sample point locations to facilitate sequential kriging. Upscaled PRFs are modified following conditional updating after each new data value is included in the estimation of parameters. Generalized sequential kriging is expected to become the main tool for real-time spatial modeling of 3D cellular models with HSP. In addition, some new developments related to the sequential kriging algorithm are included. Sequential kriging can be used for the estimation of parameters for simulation in the so-called unstructured grids.     

Interstitial voids in silica melts and implication for argon solubility under high pressures

Molecular dynamics simulations with ab initio potential under various pressures up to 11.58 GPa have been carried out to investigate the relationship between microscopic structure and solubility of Ar in silica melts. The Voronoi diagram method is used to identify interstitial voids in the structure of silica melts. We find that (1) the radius distribution of interstitial voids generally obeys the log-normal probability function; (2) the number of available interstitial voids large enough to accommodate Ar atoms decreases with increasing pressure; (3) Ar solubility increases linearly with pressure up to about 3 GPa, where Ar solubility reaches a maximum value, and then it decreases dramatically when pressure becomes higher than 5-6 GPa. The drop of Ar solubility is a result of structural continuous change but not structural transformation. These results are in good agreement with experimental measurements.     

非均匀多孔介质等效渗透率的普适表达式

多孔介质渗流是普遍的物理过程,涉及地下工程、地热开采、环境工程等各行各业,尤其是工程建设,常面临防渗问题。由于地质条件的复杂性,工程区域地层受到成岩、压实、风化、生物作用等各种影响,故渗流性质复杂,常需要对建设区域的渗流状况进行数值模拟,从而为工程的设计施工提供决策依据。数值仿真结果依赖于对地层介质关键参数的选取,但目前工程多将其视为均匀介质处理,对于介质的非均匀特性考虑较少。文章旨在研究非均质多孔介质渗透率空间分布与等效渗透率的关系。基于连续介质假定、达西定律以及非均匀多孔介质渗透率空间分布函数,建立一维到三维的达西渗流问题模型,通过求解偏微分方程和理论推导,得到基于渗透率空间分布函数的等效渗透率理论表达式,并与有限元计算的数值解进行对比分析,结果表明理论值和数值解误差很小,证明等效渗透率的表达式的合理性。利用该成果可通过多点局部渗透率的测定构建渗透率空间分布函数,从而对整体渗流区域的渗透性质进行快速计算和评估,从而简化异常复杂的工程地质模型以减少计算量需求,对于工程仿真的快速计算和结果评估有重要意义。     

Mineral potential mapping with a restricted Boltzmann machine

A restricted Boltzmann machine can be trained to encode and reconstruct training samples from a training sample population with an unknown complex probability distribution. Small probability samples can be differentiated from the training sample population due to their comparatively larger encoded and reconstructed errors. In mineral potential mapping, mineral potential areas usually take up only a small proportion of the whole mineral exploration region and have specific evidence map patterns. Assume that the whole mineral exploration region is divided into uniform cells and a restricted Boltzmann machine is then trained on all the cells. As a small proportion of the total training cells, mineral potential cells have much larger encoded and reconstructed errors compared to non-mineral potential cells. Based on the encoded and reconstructed errors of the training cells, ASC and ASE are thus defined as two mineral potential indicators for mineral potential mapping with the trained restricted Boltzmann machine. The Altay district in northern Xinjiang in China, which is linked with a complex geological setting, is chosen as a case study area. Restricted Boltzmann machines with 12 visible units and differing hidden units are constructed and trained on 9582 training cells in the study area. The ASC, ASE, posterior probability, and deposit-bearing probability are used to predict the mineral potential of each grid cell in the study area. The AUC (area under the curve), a measure of aggregated classification performance in machine learning, is applied to measure the mineral potential mapping performance of these four mineral potential indicators. The results show that the four mineral potential indicators perform similarly well. Therefore, a restricted Boltzmann machine can be trained to map mineral potentials, and the ASC and ASE are two feasible indicators for the mineral potential mapping with the trained restricted Boltzmann machine.     

Computer modeling of natural silicate melts: What can we learn from ab initio simulations

The structural and dynamical properties of four silicate liquids (silica, rhyolite, a model basalt and enstatite) are evaluated by ab initio molecular dynamics simulation using the density functional theory and are compared with classical simulations using a simple empirical force field. For a given composition, the structural parameters of the simulated melt vary little between the two calculations (ab initio versus empirical) and are in satisfactory agreement with structure data available in the literature. In contrast, ionic diffusivities and atomic vibration motions are found to be more sensitive to the details of the interactions. Furthermore, it is pointed out that the electronic polarization, as evaluated by the ab initio calculation, contributes significantly to the intensity of the infrared absorption spectra of molten silicates, a spectral feature which cannot be reproduced using nonpolarizable force field. However the vibration modes of TO₄ species and some structural details are not accurately reproduced by our ab initio calculation, shortcomings which need to be improved in the future.     

Service-oriented approach for geospatial feature discovery

Rapid increases in remote sensing capability have made remotely sensed images an importance source for intelligence analysts to discover geospatial features. The overwhelming volume of routine image acquisition has greatly outpaced the increase in the capacity of manual image interpretation by intelligence analysts, and prompted automated methods for geospatial feature extraction from high spatial resolution images. Nevertheless, existing methods focus on automatic extraction of isolated or elementary features, such as buildings and roads. A compound geospatial feature, such as a Weapon of Mass Destruction (WMD) proliferation facility, is spatially composed of elementary features (e.g., containment buildings, cooling ponds, and fences). The spatial relations among elementary features can assist the detection of compound features from images. This paper proposes a service-oriented approach for discovering compound geospatial features. The approach includes both a chaining strategy and an architecture. The chaining strategy is to discover sites of facilities by orchestrating services that compute spatial relations among elementary features. The architecture is a service-oriented framework to support the chaining for feature discovery. The approach not only takes advantages of spatial characteristics of complex features, but also enjoys the openness and flexibility of the Service-Oriented Architecture (SOA). A prototypical implementation is provided to illustrate the applicability of the approach.     

Cell to node projections: An assessment of error

Reservoir simulators typically use cell‐centered finite volume schemes and do not model directly the coupling of the flow processes with the geomechanics. Coupling of geomechanics with fluid flow can be important in many cases, but introducing fully coupled geomechanical effects in those simulators is not a trivial issue, because the geomechanics is better done by using the Galerkin vertex‐centered finite element methods by which the solid displacements are computed at the vertices of the cells. This creates difficulties in interfacing cell variables with nodal variables. Uncoupled or loosely coupled models are used by many researchers/practitioners by which a reservoir model is coupled to a geomechanical model by staggering in‐time flow and deformation via a sophisticated interface that repeatedly calls first flow and then mechanics. The method therefore requires projection of the reservoir cell variables onto the nodes of the geomechanics Galerkin finite element mesh. In this note, we attempt to quantify the errors associated with cell to node projection operations. For that purpose, we use a simple model of the pressure equation for a heterogeneous medium in one dimension. We are able to derive the exact analytical solution for this problem for both nodal and cell pressures. This allows us to compute the errors due to projection analytically, function of meshing refinement and permeability field variations. We compute upper and lower bounds for the errors, and analyze their magnitude for a variety of cases. We conclude that, in general, cell to node projection operations lead to substantial errors. Copyright © 2010 John Wiley & Sons, Ltd.     

The Wadi Mubarak belt,Eastern Desert of Egypt: a Neoproterozoic conjugate shear system in the Arabian–Nubian Shield

The Wadi Mubarak belt in Egypt strikes west–east (and even northeast–southwest) and crosscuts the principal northwest–southeast trend of the Najd Fault System in the Central Eastern Desert of Egypt. The belt therefore appears to be a structural feature that formed postdate to the Najd Fault System. In contrast, it is shown here that the deformation in the Wadi Mubarak belt can be correlated with the accepted scheme of deformation events in the Eastern Desert of Egypt and that its geometry and apparently cross-cutting orientation is controlled by a large granite complex that intruded prior to the structural evolution. Structural correlation is facilitated by a series of intrusions that intrude the Wadi Mubarak belt and resemble other intrusions in the Eastern Desert. These intrusions include: (1) an older gabbro generation, (2) an older granite, (3) a younger gabbro and (4) a younger granite. The structural evolution is interpreted to be characterized by early northwest directed transport that formed several major thrusts in the belt. This event is correlated with the main deformation event in the Eastern Desert, elsewhere known as D2. During this event the regional fabric of the Wadi Mubarak belt was wrapped around the El Umra granite complex in a west–east orientation. The Wadi Mubarak belt was subsequently affected during D3 by west–east and northwest–southeast trending sinistral conjugate strike–slip shear zones. This event is related to the formation of the Najd Fault System. Detailed resolution of superimposed shear sense indicators suggest that D3 consisted of an older and a younger phase that reflect the change of transpression direction from east-southeast–west-northwest to eastnortheast–westouthwest. The El Umra granite complex is dated here with single zircon ages to consist of intrusion pulses at 654 and 690 my. These ages conform with the interpretation that it intruded prior to D2 and that the structural pattern of the Wadi Mubarak belt was initiated early during D2.     

Lithosphere development in the Slave craton: a linked crustal and mantle perspective

The late tectonic evolution of the Slave craton involves extensive magmatism, deformation, and high temperature-low pressure (HT-LP) metamorphism. We argue that the nature of these tectonic events is difficult to reconcile with early, pre-2.7 Ga development and preservation of a thick tectosphere, and suggest that crust–mantle coupling and stabilization occurred only late in the orogenic development of the craton. The extent and repetitiveness of the tectonic reworking documented within the Mesoarchean basement complex of the western Slave, together with the development of large-volume, extensional mafic magmatism at 2.7 Ga within the basement complex argue against preservation of a widespread, thick, cool Mesoarchean tectosphere beneath the western Slave craton prior to Neoarchean tectonism. Broad-scale geological and geophysical features of the Slave craton, including orientation of an early F1 fold belt, distribution of ca. 2.63–2.62 Ga plutonic rocks, and the distribution of geochemical, petrological and geophysical domains within the mantle lithosphere collectively highlight the importance of an NE–SW structural grain to the craton. These trends are oblique to the earlier, ca. 2.7 Ga north–south trending boundary between Mesoarchean and Neoarchean crustal domains, and are interpreted to represent a younger structural feature imposed during northwest or southeast-vergent tectonism at ca. 2.64–2.61 Ga. Extensive plutonism, in part mantle-derived, crustal melting and associated HT-LP metamorphism argue for widespread mantle heat input to the crust, a feature most consistent with thin (<100 km) lithosphere at that time. We propose that the mantle lithosphere developed by tectonic imbrication of one or more slabs subducted beneath the craton at the time of development of the D1 structural grain, producing the early 2.63–2.62 Ga arc-like plutonic rocks. Subsequent collision (external to the present craton boundaries) possibly accompanied by partial delamination of some of the underthrust lithosphere, produced widespread deformation (D2) and granite plutonism throughout the province at 2.6–2.58 Ga. An implication of this model is that diamond formation in the Slave should be Neoarchean in age.     

A bond-topological approach to theoretical mineralogy: crystal structure, chemical composition and chemical reactions

Here, I describe a theoretical approach to the structure and chemical composition of minerals based on their bond topology. This approach allows consideration of many aspects of minerals and mineral behaviour that cannot be addressed by current theoretical methods. It consists of combining the bond topology of the structure with aspects of graph theory and bond-valence theory (both long range and short range), and using the moments approach to the electronic energy density-of-states to interpret topological aspects of crystal structures. The structure hierarchy hypothesis states that higher bond-valence polyhedra polymerize to form the (usually anionic) structural unit, the excess charge of which is balanced by the interstitial complex (usually consisting of large low-valence cations and (H₂O) groups). This hypothesis may be justified within the framework of bond topology and bond-valence theory, and may be used to hierarchically classify oxysalt minerals. It is the weak interaction between the structural unit and the interstitial complex that controls the stability of the structural arrangement. The principle of correspondence of Lewis acidity–basicity states that stable structures will form when the Lewis-acid strength of the interstitial complex closely matches the Lewis-base strength of the structural unit, and allows us to examine the factors that control the chemical composition and aspects of the structural arrangements of minerals. It also provides a connection between a structure, the speciation of its constituents in aqueous solution and its mechanism of crystallization. The moments approach to the electronic energy density-of-states provides a link between the bond topology of a structure and its thermodynamic properties, as indicated by correlations between average anion coordination number and reduced enthalpy of formation from the oxides for ^[6]Mg _m ^[4] Si _n O_(m+2n) and MgSO₄(H₂O) _n .     

Stochastic simulation of patterns using Bayesian pattern modeling

In this paper, a Bayesian framework is introduced for pattern modeling and multiple point statistics simulation. The method presented here is a generalized clustering-based method where the patterns can live on a hyper-plane of very low dimensionality in each cluster. The provided generalizationallows a remarkable increase in variability of the model and a significant reduction in the number of necessary clusters for pattern modeling which leads to more computational efficiency compared with clustering-based methods. The Bayesian model employed here is a nonlinear model which is composed of a mixture of linear models. Therefore, the model is stronger than linear models for data modeling and computationally more effective than nonlinear models. Furthermore, the model allows us to extract features from incomplete patterns and to compare patterns in feature space instead of spatial domain. Due to the lower dimensionality of feature space, comparison in feature space results in more computational efficiency as well. Despite most of the previously employed methods, the feature extraction filters employed here are customized for each training image (TI). This causes the features to be more informative and useful. Using a fully Bayesian model, the method does not require extensive parameter setting and tunes its parameters itself in a principled manner. Extensive experiments on different TIs (either continuous or categorical) show that the proposed method is capable of better reproduction of complex geostatistical patterns compared with other clustering-based methods using a very limited number of clusters.     

地质统计学反演及其在吉林扶余油田储层预测中的应用

地质统计学反演方法将随机建模技术与常规地震反演相结合,有效地综合地质、测井和三维地震数据,可以更加精确地描述储层的变化.在执行地质统计学反演前,首先应用稀疏脉冲约束反演,了解储层的大致分布,以求取子波和水平变差函数.地质统计学反演从井点出发,井间以原始地震数据作为硬数据,通过随机模拟的产生井间波阻抗,然后将波阻抗转换成反射系数,并用确定性反演方法求得的子波褶积产生地震道,通过反复迭代直至合成地震道与原始地震数据达到一定程度的匹配,反演结果是多个等概率的波阻抗数据体实现.反演结果符合输入数据的地质统计学特征并受地质模型的约束,它综合了测井的垂向分辨率高和地震的横向分辨率高的优势,结果的多个实现用于不确定性评价.