A model for multiphase flow and transport in porous media including a phenomenological approach to account for deformation—a model concept and its validation within a code intercomparison study

Multiphase flow processes in unsaturated cohesive soils are often affected by deformation due to swelling and shrinking as a result of varying water contents. This paper presents a model concept which is denoted ‘phenomenological’ in terms of the processes responsible for soil deformation, since the effects of deformation on flow and transport are only considered by constitutive relations that allow an adaptation of the hydraulic properties. This new model is validated in a detailed intercomparison study with two state-of-the-art models that are capable of explicitly describing the processes relevant for the deformation. A ‘numerical experiment’ with a state-of-the-art reference model is used to produce ‘measurement data’ for an inverse-modelling-based estimation of the model input parameters for the phenomenological concept.     

A new high-stress undrained ring-shear apparatus and its application to the 1792 Unzen–Mayuyama megaslide in Japan

Sassa and others in the Disaster Prevention Research Institute (DPRI), Kyoto University, developed a series of undrained ring-shear apparatus to physically simulate landslide initiation and motion, from DPRI-3 (Sassa 1992) to DPRI-7 (Sassa et al., Landslides 1(1):7–19, 2004). The maximum undrained capacities in the DPRI series ranged from 300 to 650 kPa. Sassa and others in the International Consortium on Landslides (ICL) have developed a new series of undrained ring-shear apparatus (ICL-1and ICL-2) for two projects of the International Programme on Landslides (IPL-161 and IPL-175). Both projects are supported by the Science and Technology Research Partnership for Sustainable Development Program (SATREPS) of Japan. ICL-1 was developed to create a compact and transportable apparatus for practical use in Croatia; one set was donated to Croatia in 2012. ICL-2 was developed in 2012–2013 to simulate the initiation and motion of megaslides of more than 100 m in thickness. The successful undrained capacity of ICL-2 is 3 MPa. This apparatus was applied to simulate possible conditions for the initiation and motion of the 1792 Unzen–Mayuyama megaslide (volume, 3.4?×?10⁸ m³; maximum depth, 400 m) triggered by an earthquake. The megaslide and resulting tsunami killed about 15,000 people. The Unzen Restoration Office of the Ministry of Land, Infrastructure and Transport (MLIT) of Japan systematically collected various papers and reports and published two summary leaflets: one in English in 2002 and an extended version in Japanese in 2003. Samples were taken from the source area (for initiation) and the moving area (for motion). The hazard area was estimated by the integrated landslide simulation model LS-RAPID, using parameters obtained with the ICL-2 undrained ring-shear apparatus. The estimated hazard area agrees reasonably with the landslide moving area reported in the Ministry leaflets.     

Identification of diffusion parameters in a nonlinear convection–diffusion equation using the augmented Lagrangian method

Numerical identification of diffusion parameters in a nonlinear convection–diffusion equation is studied. This partial differential equation arises as the saturation equation in the fractional flow formulation of the two-phase porous media flow equations. The forward problem is discretized with the finite difference method, and the identification problem is formulated as a constrained minimization problem. We utilize the augmented Lagrangian method and transform the minimization problem into a coupled system of nonlinear algebraic equations, which is solved efficiently with the nonlinear conjugate gradient method. Numerical experiments are presented and discussed. This work was partially supported by the Research Council of Norway (NFR), under grant 128224/431.     

Improved finite element–based limit equilibrium method for slope stability analysis by considering nonlinear strength criteria and its application in assessing the anchoring effect

The shear strength envelope of most geotechnical materials is nonlinear. In this study, the finite element–based limit equilibrium method (FELE) is improved to assess the stability of a prescribed slip surface that obeys a nonlinear failure criterion. Two nonlinear failure criteria, namely, the Barton criterion and the generalized Hoek-Brown (GHB) criterion, are implemented. A power curve model that can perfectly fit the envelope of the GHB criterion is proposed to explicitly express the shear strength from the normal stress. The algorithm of the improved FELE, which includes a nonlinear criterion, is explained in detail, and the fast convergence of the method is checked by evaluating examples. The numerical examples show that, for a smooth slip surface, FELE can calculate a greater factor of safety (FOS) than that calculated using the Morgenstern-Price (MP) method when the strength criterion of slip surface is nonlinear. In addition, FELE can determine the bell-shaped distribution of the increase in normal stress caused by anchoring measures, which cannot be considered in the MP method.     

Compositional dual mesh method for single phase flow in heterogeneous porous media—application to CO<Subscript>2</Subscript> storage

Numerical simulation of fluid flow coupled with chemical reactions has been an active field in the hydrogeology community and many formulations have been programmed into different software. In recent years, this subject has attracted increasing interest in the reservoir simulation community, partly for the application of chemical methods for hydrocarbon extraction but also for research on the geological sequestration of CO₂. In this paper, an extension to the concept of dual mesh for reactive transport modeling is presented. This approach involves two meshes, a low-resolution mesh to resolve the pressure equation and a high-resolution mesh to transport the species and to calculate the geochemical equilibrium. The main objective is to preserve the fine scale heterogeneities to reach a more accurate field behavior simulation than conventional approach which consist in performing simulations on a coarser mesh. The method is applied to a simulation of CO₂ storage in the SPE10 model that keep a high resolution of the heterogeneities.     

A 2D mixed fracture–pore seepage model and hydromechanical coupling for fractured porous media

A novel two-dimensional mixed fracture–pore seepage model for fluid flow in fractured porous media is presented based on the computational framework of finite-discrete element method (FDEM). The model consists of a porous seepage model in triangular elements bonded by unbroken joint elements, as well as a fracture seepage model in broken joint elements. The principle for determining the fluid exchange coefficient of the unbroken joint element is provided to ensure numerical accuracy and efficiency. The mixed fracture–pore seepage model provides a simple but effective tool for solving fluid flow in fractured porous media. In this paper, examples of 1D and 2D seepage flow in porous media and porous media with a single fracture or multiple fractures are studied. The simulation results of the model match well with theoretical solutions or results obtained by commercial software, which verifies the correctness of the mixed fracture–pore seepage model. Furthermore, combining FDEM mechanical calculation and the mixed fracture–pore seepage model, a coupled hydromechanical model is built to simulate fluid-driven dynamic propagation of cracks in the porous media, as well as its influence on pore seepage and fracture seepage.

     

A discretization and multigrid solver for a Darcy–Stokes system of three dimensional vuggy porous media

We develop a finite element discretization and multigrid solver for a Darcy–Stokes system of three-dimensional vuggy porous media, i.e., porous media with cavities. The finite element method uses low-order mixed finite elements in the Darcy and Stokes domains and special transition elements near the Darcy–Stokes interface to allow for tangential discontinuities implied by the Beavers–Joseph boundary condition. We design a multigrid method to solve the resulting saddle point linear system. The intertwining of the Darcy and Stokes subdomains makes the resulting matrix highly ill-conditioned. The velocity field is very irregular, and its discontinuous tangential component at the Darcy–Stokes interface makes it difficult to define intergrid transfer operators. Our definition is based on mass conservation and the analysis of the orders of magnitude of the solution. The coarser grid equations are defined using the Galerkin method. A new smoother of Uzawa type is developed based on taking an optimal step in a good search direction. Our algorithm has a measured convergence factor independent of the size of the system, at least when there are no disconnected vugs. We study the macroscopic effective permeability of a vuggy medium, showing that the influence of vug orientation; shape; and, most importantly, interconnectivity determine the macroscopic flow properties of the medium. This work was supported by the U.S. National Science Foundation under grants DMS-0074310 and DMS-0417431.     

SPH model for fluid–structure interaction and its application to debris flow impact estimation

On 13 August 2010, significant debris flows were triggered by intense rainfall events in Wenchuan earthquake-affected areas, destroying numerous houses, bridges, and traffic facilities. To investigate the impact force of debris flows, a fluid–structure coupled numerical model based on smoothed particle hydrodynamics is established in this work. The debris flow material is modeled as a viscous fluid, and the check dams are simulated as elastic solid (note that only the maximum impact forces are evaluated in this work). The governing equations of both phases are solved respectively, and their interaction is calculated. We validate the model with the simulation of a sand flow model test and confirm its ability to calculate the impact force. The Wenjia gully and Hongchun gully debris flows are simulated as the application of the coupled smoothed particle hydrodynamic model. The propagation of the debris flows is then predicted, and we obtain the evolution of the impact forces on the check dams.     

A refined garnet - biotite Fe−Mg exchange geothermometer and its application in amphibolites and granulites

A new formulation of garnet-biotite Fe–Mg exchange thermometer has been developed through statistical regression of the reversed experimental data of Ferry and Spear. Input parameters include available thermo-chemical data for quaternary Fe–Mg–Ca–Mn garnet solid solution and for excess free energy terms, associated with mixing of Al and Ti, in octahedral sites, in biotite solid solution. The regression indicates that Fe–Mg mixing in biotite approximates a symmetrical regular solution model showing positive deviation from ideality withW _FeMg ^bi =1073±490 cal/mol. H _r and S _r for the garnet-biotite exchange equilibrium were derived to be 4301 cal and 1.85 cal respectively. The resultant thermometer gives consistent results for rocks with a much wider compositional range than can be accommodated by earlier formulations.     

A micro-mechanics-based elastic–plastic model for porous rocks: applications to sandstone and chalk

A micro-mechanics-based elastic–plastic model is proposed to describe mechanical behaviors of porous rock-like materials. The porous rock is considered as a composite material composed of a solid matrix and spherical pores. The effective elastic properties are determined from the classical Mori–Tanaka linear homogenization scheme. The solid matrix verifies a pressure-dependent Mises–Schleicher-type yield criterion. Based on the analytical macroscopic yield criterion previously determined with a nonlinear homogenization procedure (Shen et al. in Eur J Mech A/Solids 49:531–538, 2015), a complete elastic–plastic model is formulated with the determination of a specific plastic hardening law and plastic potential. The micro-mechanics-based elastic–plastic model is then implemented for a material point in view of simulations of homogeneous laboratory tests. The proposed model is applied to describe mechanical behaviors of two representative porous rocks, sandstone and chalk. Comparisons between numerical results and experimental data are presented for triaxial compression tests with different confining pressures, and they show that the micro-mechanical model is able to capture main features of mechanical behaviors of porous rock-like rocks.     

SPH–DEM coupling method based on GPU and its application to the landslide tsunami. Part II: reproduction of the Vajont landslide tsunami

Acta Geotechnica - Landslide tsunamis are complex fluid–solid coupling processes that often cause enormous catastrophes. In this study, the smooth particle hydrodynamics (SPH) and discrete...     

Dissolved helium isotope ratios in ground-waters: a new technique based on gas–water re-equilibration and its application to Stromboli volcanic system

Here, a new technique for the determination of dissolved He isotope ratios in ground-waters is presented. This method is based on the extraction and subsequent equilibrium of dissolved gases in an added “host” gas phase. Ultra pure N₂ is placed in glass flasks (250 cc), containing water samples, that were hermetically sealed after their collection. After shaking in an ultrasonic bath for 10 min, an aliquot of the separated gas phase was removed from the flask for MS analysis. ³He/⁴He ratios are measured by using a modified double collector mass spectrometer (VG 5400-TFT). Helium and Ne concentrations are calculated by comparing the partial pressures of masses 4 and 20 of the samples with those of the air-standard measured by a quadrupole mass spectrometer (QMS;VG Quartz). Using He and Ne equilibrium partitioning coefficients, it is possible to calculate the amount of gas originally dissolved in the water. The technique was tested on both air-saturated waters (ASW) and thermal waters from Stromboli (Aeolian Islands, South Italy), the results of which confirmed good reproducibility (≌5%) and accuracy (≌3%) of the data. The method was then applied to three thermal water samples collected from the same volcanic area and the results compared with those of a fumarolic and a soil gas. The isotope ratios for dissolved He gave values of 4.06–4.23 Ra, which are significantly higher than those previously reported in the literature (3.0, 3.5 and 2.9 Ra) and that measured at the fumarole (3.09 Ra), suggesting a newer and higher isotopic signature for the volcanic system. The proposed method appears to be a useful tool in the determination of ³He/⁴He ratios in ground-water systems, especially when free gases are not available or are dangerous to collect.     

Determination of germanium isotopic compositions of sulfides by hydride generation MC-ICP-MS and its application to the Pb–Zn deposits in SW China

Determining Ge isotopic compositions of sulfides is important to understand the ore-forming processes. Single step anion-exchange chromatography was previously used to recover Ge from silicates and lignites. We apply this procedure to recover Ge from sulfides before determining Ge isotopic compositions by hydride generation (HG)-MC-ICP-MS. Germanium is quantitatively recovered by the proposed sample preparation method. There are no obvious isotope biases for Ge-bearing solutions containing significant amounts of Cu, Sn, and W. However, δ⁷⁴Ge values show obvious shifts if the solutions contain high Zn, Pb, and Sb, which is possibly attributed to suppression of germane formation that fractionates Ge isotopes. The long-term reproducibility for Ge standard solution is about ± 0.18‰ for δ⁷⁴Ge. Spex and Merck standard solutions yield mean δ⁷⁴Ge values of − 0.70 ± 0.19‰ and − 0.36 ± 0.08‰, respectively. The calculated δ⁷⁴Ge value (− 5.13‰) of sphalerite standard based on doping experiments is indistinguishable from those of sphalerite without doping (− 5.05‰ and − 5.01‰). Sulfides from the Jinding, Shanshulin, and Tianqiao Pb–Zn deposits in SW China have δ⁷⁴Ge values of − 4.94‰ to + 2.07‰. The paragenetic sequence of sulfides from the Shanshulin and Tianqiao Pb–Zn deposits is pyrite, sphalerite and galena from early to late. Sulfides from the same ore show a trend of δ⁷⁴Ge_pyrite < δ⁷⁴Ge_sphalerite < δ⁷⁴Gegalena, which may be controlled by the kinetic or Rayleigh fractionation.     

Unload–load displacement response ratio parameter and its application in prediction of debris landslide induced by rainfall

As the traditional displacement value of a landslide is very easy to be affected by rainfall, it is very difficult to establish a stable and uniform destabilized criterion of landslide in terms of the displacement value. So, it determines that establishment of an effective and stable dynamic displacement prediction parameter is very important in forecast of the debris landslides caused by rainfall. In order to determine this kind of prediction parameter, this paper first completes analysis on the relationship between the destabilized mechanism of the debris landslide and the rainfall dynamic rules. The relationship above shows that the periodical change value of rainfall can be taken as the dynamic unload–load parameter (ULP) of landslide, and the homologous change value of mensal landslide displacement can be taken as the stability displacement response parameter (DRP). Then, on the basis of the relationship between the ULP and the stability DRP of this kind of landslide, the unload–load displacement response ratio (ULDRR) appraisal parameter of this kind of landslides is established in this paper. Finally, the stability of typical debris landslides in China has been systematically studied by means of ULDRR appraisal parameter and model. We find that the ULDRR values conform to the evolutional rule of slope deformation and instability. So, it has been proved that the ULDRR parameter and the appraisal model are suitable and effective for prediction and evaluation of stability and evolution rule of rainfall-induced landslides.     

Thermogravimetry-differential thermal analysis coupled with chromatography as a thermal simulation experimental method and its application to gaseous hydrocarbons from different source rocks

In this paper a thermogravimetry-differential thermal analysis method coupled with chromatography （TG-DTA-GC） has been adopted to simulate the generation of gaseous hydrocarbons from different hydrocarbon source rocks such as coals, mudstones, and carbonate rocks with different maturities. The temperature programming for thermal simulation experiment is 20℃/min from ambient temperature to 700℃. As viewed from the quantities and composition of generated gaseous hydrocarbons at different temperatures, it is shown that low-mature coal has experienced the strongest exothermic reaction and the highest loss of weight in which the first exothermic peak is relatively low. Low-mature coal samples have stronger capability of generating gaseous hydrocarbons than high-mature samples. The amounts and composition of gaseous hydrocarbons generated are closely related not only to the abundance of organic carbon in source rocks, but also to the type of kerogen in the source rocks, and their thermal maturity. In the present highly mature and over-mature rock samples organic carbon, probably, has already been exhausted, so the production of gaseous hydrocarbons in large amounts is impossible. The contents of heavy components in gaseous hydrocarbons from the source rocks containing type- Ⅰ and - Ⅱ kerogens are generally high ; those of light components such as methane and ethane in gaseous hydrocarbons from the source rocks with Ⅲ-type kerogens are high as well. In the course of thermal simulation of carbonate rock samples, large amounts of gaseous hydrocarbons were produced in a high temperature range.