Another look at the conceptual fundamentals of porous media upscaling

We suggest a critical look at the epistemic foundations of the porous media upscaling problem that focuses on conceptual processes at work and not merely on form manipulations. We explore the way in which critical aspects of scientific methodology make their appearance in the upscaling context, thus generating useful effective parameters in practice. The fons et origo of our approach is a conceptual blending of knowledge states that requires the revision of the traditional method of scientific argument underlying most upscaling techniques. By contrast to previous techniques, the scientific reasoning of the proposed upscaling approach is based on a stochastic model that involves teleologic solutions and stochastic logic integration principles. The syllogistic form of the approach has important advantages over the traditional reasoning scheme of porous media upscaling, such as: it allows the rigorous derivation of the joint probability distributions of hydraulic gradients and conductivities across space; it imposes no restriction on the functional form of the effective parameters or the shape of the probability laws governing the random media (non-Gaussian distributions, multiple-point statistics and non-linear models are automatically incorporated); it relies on sound methodological principles rather than being ad hoc; and it offers the rational means for integrating the multifarious core knowledge bases and uncertain site-specific information sources about the subsurface system. Previous upscaling results are derived as special cases of the proposed upscaling approach under limited conditions of porous media flow, a fact that further demonstrates the generalization power of the approach. Our hope is that looking at the upscaling problem in this novel way will direct further attention to the methodological exploration of the problem at the length and the detail that it deserves.I would like to thank Drs. A. Kolovos and D.T. Hristopulos for their valuable comments. The work was supported by grants from the Army Research Office (Grant no. DAAG55–98–1-0289) and the National Institute of Environmental Health Sciences (P42-ES05948 & P30-ES10126).     

Application of stress-pore pressure coupling theory for porous media to the Xinfengjiang reservoir earthquakes

Theory of the coupling of stress-pore pressure in the saturated, elastic porous media is used in the study of the formation mechanism of the Xinfengjiang reservoir-induced earthquakes. Based on the results, it is believed that compared with the mechanism of additional stress in the vicinity of the reservoir, the mechanism of the coupling of additional stress and pore pressure may be more well-founded for the occurrence of reservoir-induced earthquakes.     

关于波浪作用下粉土质海床中共振现象的解释

本文详细讨论了粉土质床在波浪作用下所呈现共振现象的力学机制。利用有限深海床下波浪载荷对土层响应的研究，系统地比较了理论计算结果和实验结果。提出在波浪作用下粉土质土层中存在着一硬土层，从而引发Ｂｒａｇｇ共振。     

Seismic Wave Propagation and Excitation in Multi-layered Media with Irregular Interfaces Part (Ⅰ): SH Case

Study of seismic wave excitation and propagation in laterally heterogeneous media was an active and important subject in seismology in the past two decades, numerous analytical and numerical efforts have been made in this research field. In this article, I have, first, made a brief review on those developments and then introduced and summarized a unified and efficient method, global generalized reflection-transmission (abbreviated to R/T thereafter) matrices method, for synthetic seismograms in multi-layered media with irregular interfaces developed by the author [24~26]. As demonstrated in this article, this method could be regarded as an extension of the generalized R/T coefficients method for the horizontally layered case [2,5] to the layered media with irregularly shaped interfaces by incorporating the T matrices technique [27,28]. Because of the use of a recursive scheme in computing the global generalized R/T matrices, this method is efficient, particularly for the case with a large number of irre     

Numerical modeling of two-phase flow in heterogeneous permeable media with different capillarity pressures

Contrast in capillary pressure of heterogeneous permeable media can have a significant effect on the flow path in two-phase immiscible flow. Very little work has appeared on the subject of capillary heterogeneity despite the fact that in certain cases it may be as important as permeability heterogeneity. The discontinuity in saturation as a result of capillary continuity, and in some cases capillary discontinuity may arise from contrast in capillary pressure functions in heterogeneous permeable media leading to complications in numerical modeling. There are also other challenges for accurate numerical modeling due to distorted unstructured grids because of the grid orientation and numerical dispersion effects. Limited attempts have been made in the literature to assess the accuracy of fluid flow modeling in heterogeneous permeable media with capillarity heterogeneity. The basic mixed finite element (MFE) framework is a superior method for accurate flux calculation in heterogeneous media in comparison to the conventional finite difference and finite volume approaches. However, a deficiency in the MFE from the direct use of fractional flow formulation has been recognized lately in application to flow in permeable media with capillary heterogeneity. In this work, we propose a new consistent formulation in 3D in which the total velocity is expressed in terms of the wetting-phase potential gradient and the capillary potential gradient. In our formulation, the coefficient of the wetting potential gradient is in terms of the total mobility which is smoother than the wetting mobility. We combine the MFE and discontinuous Galerkin (DG) methods to solve the pressure equation and the saturation equation, respectively. Our numerical model is verified with 1D analytical solutions in homogeneous and heterogeneous media. We also present 2D examples to demonstrate the significance of capillary heterogeneity in flow, and a 3D example to demonstrate the negligible effect of distorted meshes on the numerical solution in our proposed algorithm.     

Application of implicit sub-time stepping to simulate flow and transport in fractured porous media

In general, the accuracy of numerical simulations is determined by spatial and temporal discretization levels. In fractured porous media, the time step size is a key factor in controlling the solution accuracy for a given spatial discretization. If the time step size is restricted by the relatively rapid responses in the fracture domain to maintain an acceptable level of accuracy in the entire simulation domain, the matrix tends to be temporally over-discretized. Implicit sub-time stepping applies smaller sub-time steps only to the sub-domain where the accuracy requirements are less tolerant and is most suitable for problems where the response is high in only a small portion of the domain, such as within and near the fractures in fractured porous media. It is demonstrated with illustrative examples that implicit sub-time stepping can significantly improve the simulation efficiency with minimal loss in accuracy when simulating flow and transport in fractured porous media. The methodology is successfully applied to density-dependent flow and transport simulations in a Canadian Shield environment, where the flow and transport is dominated by discrete, highly conductive fracture zones.     

考虑土体固液二相性质的地下管线地震反应研究

本文将管线周围的土体视为固-液二相介质，采用考虑地震过程中土体内孔隙水压力的增长和消散的有效应力分析方法，并以非线性的土体本构模型模拟土体动力特性的改变以及在孔隙水压作用下的变形，以求接近土体的真实地震反应。研究表明随着土体软化程度的不同，受到土体约束的管线应力亦发生相应变化。文中详细研究了地震动峰值、管线直径、行波波速和入射角度等对管线应力的影响。     

A semi-empirical approach to model pressure dependence of elastic moduli in granular media accounting for variations of coordination-number and Poisson-ratio

The effective medium theory based on the Hertz–Mindlin contact law is the most popular theory to relate dynamic elastic moduli (or elastic velocities) and confining pressure in dry granular media. However, many experimental results proved that the effective medium theory predicts pressure trends lower than experimental ones and over-predicts the shear modulus. To mitigate these mispredictions, several evolutions of the effective medium theory have been presented in the literature. Among these, the model named modified grain contact theory is an empirical approach in which three parametric curves are included in the effective medium theory model. Fitting the parameters of these curves permits to adjust the pressure trends of the Poisson ratio and the bulk modulus. In this paper, we present two variations of the modified grain contact theory model. First, we propose a minor modification in the fitting function for the porosity dependence of the calibration parameters that accounts for non-linearity in the vicinity of the critical porosity. Second, we propose a major modification that reduces the three-step modified grain contact theory model to a two-step model, by skipping the calibration parameter–porosity fit in the model and directly modelling the calibration parameter–pressure relation. In addition to an increased simplicity (the fitting parameters are reduced from 10 to 6), avoiding the porosity fit permits us to apply the model to laboratory data that are not provided with accurate porosity measurements. For this second model, we also estimate the uncertainty of the fitting parameters and the elastic velocities. We tested this model on dry core measurements from literature and we verified that it returns elastic velocity trends as good as the original modified grain contact theory model with a reduced number of fitting parameters. Possible developments of the new model to add predictive power are also discussed.     

Isolation of plane shear wave using water saturated trench barrier

The article presents a theoretical investigation of the propagation of normally and obliquely incident plane shear waves past a rectangular trench filled up with water saturated soil sandwiched between anisotropic elastic media. The motivation for this work is due to the effectiveness of the isolation of waves by the in-filled rectangular trench. Unlike the most of the previous researchers, this model considers the soil–structure interaction effects and directly determines the influence of barrier in the form of in-filled trench on the mode of wave propagation. It is of interest to determine the reflection and transmission coefficients, and the energy partition distribution of shear waves in the in-filled rectangular trench showing the influence of barrier on the propagation of waves. An extensive parametric study through numerical computation is carried out to investigate the influence of the material properties of the in-filled trench and the amplitude ratios on shear waves. The in-filled trench barrier directly declines the intensity of waves significantly in such a way that the waves do not create any hazards to the nearby structures, if exists at all.     

Structure of residual oil as a function of wettability using pore-network modelling

In the water flooding of mixed-wet porous media, oil may drain down to relatively low residual oil saturations (S_or). Various studies have indicated that such low saturations can only be reached when oil layers in pore corners are included in the pore-scale modelling. These processes within a macroscopic porous medium can be modelled at the pore-scale by incorporating the fundamental physics of capillary dominated displacement within idealised pore network models. Recently, the authors have developed thermodynamic criteria for oil layer existence in pores with non-uniform wettability which takes as input geometrically and topologically representative networks, to calculate realistic S_or values for mixed-wet and oil-wet sandstones [16, 21]. This previous work is developed in this paper to include (i) the visualisation of the 3D structure of this residual oil, and (ii) a statistical analysis of this “residual/remaining” oil. Both the visualisation and the statistical analysis are done under a wide range of wettability conditions, which is reported for the first time in this paper.The structure of residual oil for strongly water wet systems is well known (where residual = remaining oil) and our model agrees with this but this structure changes radically for mixed wet systems (where residual ≠ remaining) and this has not yet been visualised experimentally. We find that for more water-wet systems high final residual oil saturations are reached at relatively small amounts of water injected and this oil is present in the pores as bulk oil. On the other hand, for more oil-wet systems we find a slow decrease of the amount of remaining oil with increasing amounts of injected water. During the process, the remaining connectivity of the oil phase is increasingly provided by oil layers only, hence the slow drainage. The final residual oil saturation, only reached in the theoretical limit of an infinite amount of injected water, is almost entirely contained in large number of (relatively low volume) oil layers, which are present in pores of most radius sizes.