A mathematical and numerical model for reactive fluid flow systems

We formulate mathematical and numerical models for multispecies, multi-phase and non-isothermal reactive fluid flow in porous media focusing on the chemical reactions and the transport of solutes. Mass conservation and stability in the time integration are emphasized. We use cell-centered finite volume differencing in space and an implicit Runge-Kutta method in time. Assuming two space dimensions, we introduce flux approximation for arbitrarily shaped convex quadrilaterals. On equidistant and variable sized rectangular grids we choose limited κ= related schemes to approximate the advective flux and the central difference scheme for the diffusive flux. On non-rectangular grids we recommend the VF9 scheme for the estimation of the diffusive flux. Our model exists as a code. This revised version was published online in July 2006 with corrections to the Cover Date.     

A transient finite element analysis of linear viscoelastic material model

Since the attenulation of propagating waves through soil/rock is related to the localized material properties as well as the strain developed, the commonly used Rayleigh-type damping model and its variations are not suitable for dynamic finite element analysis of such materials. A linear viscoelastic material model based on the concept of the relaxation spectrum is manipualted in place of the damping model in this paper. The method proposed by Day and Minster¹¹ to transform the convolutional form of the stress–strain relationship to a set of differential operators using the Pade approximant method is generalized to non-scalar waves and implemented for transient finite element analyses. A time-marching scheme is also proposed to incorporate the resultant differential operators into the governing equation of motion. The accuracy related to the Pade approximant method and the time-marching scheme is investigated by critically analysing some scalar wave propagation problems. The proposed technique is further verified using two one-dimensional stress wave propagation problems and a two-dimensional transient propagating wave through an unbounded linear viscoelastic medium. Some encouraging results have been obtained using the proposed technique and guidelines for using this technique are also presented. Comparisons of analytical solutions obtained by Fourier synthesis and numerical results have been provided.     

非均匀层状介质一维波动方程精确解的有限差分算法

平面波的传播问题通常可以归结为一维波动方程的定解问题。在非均匀介质中,即使简单的一维波动方程也需要借助于数值方法获得近似解。3层5点古典差分格式是计算偏微分方程一种常用算法,作为一种显式迭代格式,需要满足稳定性条件 ,其中 为波速, 为空间采样间隔, 为时间采样间隔。当 时, ,古典差分格式达到临界稳定状态。在这种情况下,平面波在 时间内的传播距离恰好等于空间采样间隔,差分格式真实地反映了平面波的传播原理,因而可以得到一维波动方程的精确解。但是,由于在非均匀介质中存在不连续的波阻抗界面,此方法不适于计算非均匀介质的波场。为了将临界稳定情况下的古典差分格式推广应用至非均匀层状介质,提出了一种能够处理波阻抗界面的有限差分格式,并应用傅里叶分析法得到其稳定性条件。模型算例验证了此算法的正确性。     

On the reliability of different methods of seismic hazard assessment in Greece

Historical and present century instrumental data have been used to determine seismic hazard in 35 sites of Greece by the application of Cornell's method (Cornell, 1968) and the mean value method. The macroseismic intensity has been considered as a measure of seismic hazard. Comparison of the results of the two methods showed that, in general, the mean value method gives higher values, particularly for low probabilities of exceedance. In addition, for some sites, the differences of the expected intensities resulting from the two methods, indicate that finer tuning of the seismogenic souce model is required, or suggest time dependence. Although each one of these methods has its own merits, the method based on seismic zonation (Cornell's method) has several advantages and must be preferred when an accurate zonation is possible by the use of macroseismic and instrumental seismic data, together with geological and geomorphological information. However, reliable estimates of seismic hazard at a particular site require work on a microzoning scale, incorporating historical, archaeological, and recent geological data.Paper presented at the 21st General Assembly of the European Seismological Commission held in Sofia, 1988.     

Valent state and coordination of cobalt Ions in beryl and chrysoberyl crystals

We have studied the polarized optical absorption and EPR spectra of Co-doped beryls grown by hydrothermal, flux, and gas-transport methods, and chrysoberyl grown by the Czochralski method. In beryls three groups of bands, belonging to three various Co centers, were distinguished by analysis of the absorption band intensities. The first group, bands with maxima at 22 220 (E c), 17 730 (E c), and 9090 (E c), 7520 (E c) cm^–1 are due to Co²⁺ in octahedral site of Al³⁺. The second group is bands at 18 940, 18 250, 17 700 (E c), 18 300, 17 700, 17 000 (E c) and 8830 (E c), 7350 (E c) cm^–1 and 5320 (E c), 3880 (E c) cm^–1, which are caused by Co²⁺ in tetrahedral site of Be²⁺. A weak wide band in flux and gas-transport beryl in the region of 12 500–8300 cm^–1 (E , c) is related to Co³⁺ in octahedral Al³⁺ site. In hydrothermal beryl, bands 13 200 (E c), 10 900 (E c), and 8500 (E c) cm^–1 are caused by an uncontrolled impurity of Cu²⁺ ions. For Co-doped chrysoberyl one type of center of Co has been established: Co²⁺ in the octahedral site of Al³⁺. In the approximation of the trigonal field with regard to Trees correction, the energy levels of Co²⁺ have been calculated in octahedral and tetrahedral coordination. There is good agreement between the obtained experimental and calculated data. The polarization dependence of the optical absorption bands is explained well in terms of the spin-orbit interaction.     

Numerical Homogenization of the Rigidity Tensor in Hooke''s Law Using the Node-Based Finite Element Method

Combining a geological model with a geomechanical model, it generally turns out that the geomechanical model is built from units that are at least a 100 times larger in volume than the units of the geological model. To counter this mismatch in scales, the geological data model's heterogeneous fine-scale Young's moduli and Poisson's ratios have to be upscaled to one equivalent homogeneous coarse-scale rigidity. This coarse-scale rigidity relates the volume-averaged displacement, strain, stress, and energy to each other, in such a way that the equilibrium equation, Hooke's law, and the energy equation preserve their fine-scale form on the coarse scale. Under the simplifying assumption of spatial periodicity of the heterogeneous fine-scale rigidity, homogenization theory can be applied. However, even then the spatial variability is generally so complex that exact solutions cannot be found. Therefore, numerical approximation methods have to be applied. Here the node-based finite element method for the displacement as primary variable has been used. Three numerical examples showing the upper bound character of this finite element method are presented.     

Analysis of oil lens removal by extraction through a seepage face

Removal of LNAPL (oil) from an aquifer is described using a multiphase flow model. At the well boundary seepage face conditions are imposed. These conditions are implemented in a numerical model and withdrawal in a twodimensional domain is simulated for two different geometries of the oil lens and for varied values of the physical parameters. Assuming vertical equilibrium, the oil flow equation is reduced by vertical integration. The well boundary condition is approximated by imposing zero oil lens thickness. Similarity solutions of the reduced equations for the two geometries show good agreement with the numerical results in most cases.     

Using numerical modelling to evaluate tsunami hazard near the Kuril Island

A sequence of computer experiments is used to study questions concerning the tsunami problem as a quantitative estimate of tsunami danger, detailed geographical tsunami classification, determination of the parameters of critical tsunami waves, and the conditions of their development. We call a wave critical, if its impact on the coast is most hazardous.Using the Middle Kuril Island as an example, we present the results of a computer experiment which includes determining the wavefields on the shelf and estimating the effects connected with the deep-water Bussol and Diana Straits.Numerical simulation of tsunami waves of different sources permits the assessment of the extent of tsunami danger in different areas of the coastal zone of Simushir Island, depending on the location of the focus zone and their geometry.The major singularities of the wavefield arise in the zones of the deep-water straits. The distribution of the amplification factors is determined by both the global parameters of the wavefields and the local properties of individual harbours. The results obtained for a particular harbour in the northern part of Simushir Island, formed the basis for the quantitative estimate of tsunami danger for this area.     

Epithermal gold veins in a caldera setting: Banská Hodruša, Slovakia

The central zone of the large Miocene tiavnica stratovolcano in the Western Carpathians hosts epithermal Au mineralization of intermediate-sulfidation type, located at deep levels of the historic Rozália base-metal mine at Banská Hodrua. The Au mineralization occurs as subhorizontal veins at the base of pre-caldera andesites, close to the roof of a subvolcanic granodiorite intrusion. The veins are dismembered by a set of quartz–diorite porphyry sills and displaced by the younger, steeply dipping, Rozália base-metal vein, and parallel structures. The base-metal vein structures are related to resurgent horst uplift in the caldera center. The Au mineralization formed during two stages. Based on fluid inclusion evidence, both stages formed from fluids of low salinity (0–3 wt% NaCl eq.), which underwent extensive boiling at moderate temperatures (280–330°C). Variable pressure conditions (39–95 bars, neglecting the effect of CO₂) indicate continual opening of the system and a transition from suprahydrostatic towards hydrodynamic conditions at shallow depths (~550 m). The fluid inclusions of the Rozália base-metal vein show homogenization temperature peaks at ~285 and 187°C and salinities between 1 and 4 wt% NaCl eq. Precipitation of Au is considered to be the result of prolonged boiling of fluids and associated decrease in Au solubility. Oxygen and hydrogen isotope data for quartz and carbonate from the Au veins show a relatively homogeneous fluid composition (–2.7 to 1.1¹⁸O, –78 to –62D). The combined ¹⁸O_fluid and D_fluid values suggest a mixed character of fluids, falling between the fields of typical magmatic and meteoric water influenced by ¹⁸O_fluid shift due to fluid–rock isotopic exchange. End stages of open-system boiling and fractionation could have been reached, at least locally. Significantly lower isotopic composition of meteoric fluids associated with Au mineralization compared to those associated with the intrusion-related mineralizations could have resulted from changing paleoclimate and/or analytical problems of extraction of water from fluid inclusions. The proposed genetic model for the Au deposit at Rozália mine highlights the importance of hydrothermal activity during the early stage of caldera collapse. Caldera subsidence established new, convective, fluid-flow paths along marginal caldera faults, which acted as infiltration zones. Major metal precipitation occurred within subhorizontal structures that formed as the result of a collapse-related stress field. A shallow, differentiated magma chamber at the base of the volcano was the likely source of heat and magmatic components for the mineralizing fluids.Editorial handling: S. Nicolescu     

Finite element modeling of wave propagation problems in multilayered soils resting on a rigid base

A new finite element scheme is proposed, in this paper, for solving two-dimensional wave propagation problems in multilayered soils resting on a rigid base. The multilayered soils are treated as multiple horizontal layers of lateral infinite extension in geometry. Since these horizontal layers can be truncated by two artificially truncated vertical boundaries, two high-order artificial boundary conditions are applied for propagating the incoming waves from the interior domain into the far field of the system. Both the semi-analytical method and the truncated boundary migration procedure are used to derive the high-order artificial boundary conditions, which are comprised of a physically meaningful dashpot and a generalized energy absorber. The main advantage of using the proposed finite element scheme is that the derived artificial boundary condition can be straightforwardly implemented in the finite element analysis, without violating the band/sparse structure of the conventional finite element equation. The related numerical examples have demonstrated that the proposed finite element scheme is of high accuracy in dealing with wave propagation problems in multiple horizontal layers.     

Isotope geochemistry of the Tieluping silver-lead deposit, Henan, China: A case study of orogenic silver-dominated deposits and related tectonic setting

The Tieluping silver deposit, which is sited along NE-trending faults within the high-grade metamorphic basement of the Xionger Terrane in the Qinling orogenic belt, is part of an important, recently discovered Mesozoic orogenic-type Ag-Pb belt. Ore formation includes three stages: an early barren quartz-pyrite stage (E), an intermediate polymetallic sulfide ore stage (M), and a late barren carbonate stage (L). Carbon, sulfur and lead isotope systematics indicate that the E-stage fluids are deeply sourced; the L-stage fluids are shallow-sourced meteoric water; whereas the M-stage fluids are a mix of deep-sourced and shallow-sourced fluids. Sulfur and lead isotope data show that the ore-forming fluids must have originated from a source with elevated radiogenic lead and low ³⁴S values, that differs significantly from exposed geologic units in the Xionger Terrane, the lower crust and the mantle. This supports the view that the carbonate-shale-chert sequences of the Guandaokou and Luanchuan Groups south of the Machaoying fault might be the favorable sources, although little is known about their isotopic compositions. A tectonic model that combines collisional orogeny, metallogeny and hydrothermal fluid flow is proposed to explain the formation of the Tieluping silver deposit. During the Mesozoic collision between the North China Craton and South China Block (Early-Mid Triassic Indosinian Orogeny), crustal slabs containing the carbonate-shale-chert sequences of the Guandaokou and Luanchuan Groups, locally rich in organic matter (carbonaceous shale), were thrust northwards beneath the Xionger Terrane along the Machaoying fault. Metamorphic devolatilisation of this underthrust slab probably provided the ore-forming fluids to develop the Ag-Pb ore belt, which includes the Tieluping silver deposit. Fluids and magmas were emplaced during extensional stages related to the Jurassic-Cretaceous Yanshanian Orogeny.Editorial Handling: B. Lehmann     

超声波在粘弹性混凝土介质中传播机理研究

混凝土是一种含有骨料、水泥浆、钢筋、波纹管包裹的预应力孔道及空洞、孔隙的多相非均匀复合材料,作为一种粘弹性介质,超声在混凝土中传播机理比较复杂,常规的弹性声波方程不能确切地模拟超声传播方式。这里从粘弹性介质材料性质出发,推导了基于Kelvin粘弹性介质模型的高阶有限差分方程,通过建立几种粘弹性混凝土介质数值模型,模拟了超声波在混凝土中的传播过程,分析了含空洞、裂隙等不同缺陷的混凝土介质中超声波的波形特性,讨论了缺陷部位波形的变化规律,探讨了空洞、裂隙等不同缺陷对超声传播机理的影响以及能量分布的差异,为准确判断识别混凝土内部不同结构的缺陷提供科学借鉴。     

The eastern continuation of the Cadomian orogen: U–Pb zircon evidence from Saxo-Thuringian granitoids in south-western Poland and the northern Czech Republic

We report U–Pb single zircon ages from three pre-Variscan granitoids in the NE part of the Bohemian Massif. The Platerówka granodiorite from the Lausitz-Izera Unit, the Polish Sudetes, has been dated at 533±9 Ma. The Bitouchov granite form the SW part of the South Krkonoe Unit, the Czech Sudetes, gave an age of 540+11/–10 Ma, and the Wdroe granodiorite in the Fore-Sudetic Block yielded 548±9 Ma. All these latest Vendian/Early Cambrian granitoids represent the post-tectonic expression of a late Proterozoic Cadomian orogenic cycle and demonstrate the eastward extent of the Cadomian basement into the Variscan orogen. Granodiorites of similar age have so far been reported from Brittany and especially from the Saxo-Thuringian Terrane to the NE and SW of the Elbe Fault Zone. We conclude that the Saxo-Thuringian Terrane extends across the Elbe and Sudetic Marginal Fault Zones into the Fore-Sudetic Block.     

Hybrid discretization of multi-phase flow in porous media in the presence of viscous,gravitational, and capillary forces

Multi-phase flow in porous media in the presence of viscous, gravitational, and capillary forces is described by advection diffusion equations with nonlinear parameters of relative permeability and capillary pressures. The conventional numerical method employs a fully implicit finite volume formulation. The phase-potential-based upwind direction is commonly used in computing the transport terms between two adjacent cells. The numerical method, however, often experiences non-convergence in a nonlinear iterative solution due to the discontinuity of transmissibilities, especially in transition between co-current and counter-current flows. Recently, Lee et al. (Adv. Wat. Res. 82, 27–38, 2015) proposed a hybrid upwinding method for the two-phase transport equation that comprises viscous and gravitational fluxes. The viscous part is a co-current flow with a one-point upwinding based on the total velocity and the buoyancy part is modeled by a counter-current flow with zero total velocity. The hybrid scheme yields C¹-continuous discretization for the transport equation and improves numerical convergence in the Newton nonlinear solver. Lee and Efendiev (Adv. Wat. Res. 96, 209–224, 2016) extended the hybrid upwind method to three-phase flow in the presence of gravity. In this paper, we present the hybrid-upwind formula in a generalized form that describes two- and three-phase flows with viscous, gravity, and capillary forces. In the derivation of the hybrid scheme for capillarity, we note that there is a strong similarity in mathematical formulation between gravity and capillarity. We thus greatly utilize the previous derivation of the hybrid upwind scheme for gravitational force in deriving that for capillary force. Furthermore, we also discuss some mathematical issues related to heterogeneous capillary domains and propose a simple discretization model by adapting multi-valued capillary pressures at the end points of capillary pressure curves. We demonstrate this new model always admits a consistent solution that is within the discretization error. This new generalized hybrid scheme yields a discretization method that improves numerical stability in reservoir simulation.     

The Andra Couplex 1 Test Case: Comparisons Between Finite-Element, Mixed Hybrid Finite Element and Finite Volume Element Discretizations

We present here results for the Andra Couplex 1 test case, obtained with the code Cast3m. This code is developped at the CEA (Commissariat l'nergie atomique) and is used mainly to solve problems of solid mechanics, fluid mechanics and heat transfers. Different types of discretization are available, among them finite element, finite volume and mixed hybrid finite element method. Cast3m is also a componant of the platteform Alliances (co-developped by Andra, CEA), which will be used by Andra for the safety calculation of an underground waste disposal in year 2004. We solve the Darcy equation for the water flow and a convection–diffusion transport equation for the Iodine 129 which escapes from a repository cave into the water. The water flow is calculated with a MHFE discretization. It is shown that this method provides sharp results even on relatively coarse grids. The convection–diffusion transport equation is discretized with FE (Finite Element), MHFE (Mixed Hybrid Finite Element) and FV (Finite Volume) methods. In our comparison, we point out the differences of these methods in term of accuracy, respect of the maximum principle and calculations cost. Neither the finite element nor the mixed hybrid finite element approach respects the maximum principle. This results in the presence of negative concentrations near the repository cave, whereas FV calculations respect the monotonicity. We show that mass lumping techniques suppress this problem but with strong restrictions on the grid. FE and MHFE approaches are more accurate than FV for the diffusion equation, but the overall results are equivalent since the advective terms are dominant in the far field and are discretized with centered schemes. We conclude by studying the influence of the grid: a very fine grid near the repository solves almost all the problems of monotonicity, without employing mass lumping techniques. We also observed a very important increase of the accuracy on a structured grid made up of rectangles.     

移动荷载下瞬态振动的三维移动坐标有限元分析

针对移动荷载引起地基振动问题的特点,在随荷载移动坐标系下建立有限元方程进行分析,能够与常规有限元方法较好地符合。建立了可用于移动坐标有限元法的黏弹性边界,从而有效地模拟波在边界的透射。以Euler-Bernoulli梁模拟轨道和路基的作用,以三维实体单元模拟黏弹性分层地基,得到的数值模拟结果能够与瑞典Ledsgård地区高速铁路实测数据较好地吻合,表明移动坐标有限元法可以有效地分析此类问题。     

An integrated linear/non-linear flow model for the conduit-fissure-pore media in the karst triple void aquifer system

Most karstic aquifer media may be characterized as the triple-void media with highly-varied hydraulic properties, including matrix pore, fissure and conduit, in which liner flow may co-exist with non-linear flow. In this paper, an attempt is made to couple linear flow with non-linear flow in a single unified flow governing equations by introducing the concept of equivalent hydraulic conductivity (EHC) and deriving a general Darcys law for various flow. The expression of EHC in the karst conduit and fissure are also derived. The procedures of numerical implementation are demonstrated via an ideal model and a case study of karst aquifer system in the Beishan Ore Formation area, Guangxi Autonomous Region, China.     

Influence of Heterogeneity of Mechanical Properties on Hydraulic Fracturing in Permeable Rocks

Summary Numerical simulations of circular holes under internal hydraulic pressure are carried out to investigate the hydraulic fracture initiation, propagation and breakdown behavior in rocks. The hydraulic pressure increases at a constant rate. The heterogeneity of the rocks is taken into account in the study by varying the homogeneity index. In addition, the permeability is varied with the states of stress and fracture. The simulations are conducted by using a finite element code, F-RFPA^2D, which couples the flow, stress and damage analyses. The simulation results suggest that the fracture initiation and propagation, the roughness of the fracture path and the breakdown pressure are influenced considerably by the heterogeneity of rocks. The hole diameter elongation and the stress field evolution around the fracture tip during the fracture propagation can also provide useful information for the interpretation of the hydraulic fracturing behaviour.