Cluster evolution in steady-state two-phase flow in porous media

We report numerical studies of the cluster development of two-phase flow in a steady-state environment of porous media. This is done by including biperiodic boundary conditions in a two-dimensional flow simulator. Initial transients of wetting and non-wetting phases that evolve before steady-state has occurred, undergo a cross-over where every initial patterns are broken up. For flow dominated by capillary effects with capillary numbers in order of $10^{-5}$, we find that around a critical saturation of non-wetting fluid the non-wetting clusters of size $s$ have a power-law distribution $n_s \sim s^{-\tau}$ with the exponent $\tau = 1.92 \pm 0.04$ for large clusters. This is a lower value than the result for ordinary percolation. We also present scaling relation and time evolution of the structure and global pressure.Comment: 12 pages, 11 figures. Minor corrections. Accepted for publication in Phys. Rev.

Inflation oder Deflation?

Auf die Finanzkrise haben die Zentralbanken und die Regierungen mit ungewöhnlichen Maßnahmen reagiert. Die Geldpolitik senkt die Zentralbankzinsen bis auf die Nullgrenze, die Wirtschaftspolitik ist bemüht, mit riesigen Konjunkturprogrammen die Rezession zu bekämpfen. Diese Maßnahmen könnten inflationäre Prozesse auslösen. Einige Experten sehen sie jedoch als unverzichtbare Instrumente gegen anhaltende Stagnation und halten Deflation für eine wesentlich größere Gefahr. Entscheidend ist der Zeitpunkt im Prozess der konjunkturellen Erholung, an dem die Zentralbanken die reichlich angebotene Liquidität wieder zurücknehmen müssen

Outgassing of icy bodies in the Solar System - II. Heat transport in dry, porous surface dust layers

In this work, we present a new model for the heat conductivity of porous dust layers in vacuum, based on an existing solution of the heat transfer equation of single spheres in contact. This model is capable of distinguishing between two different types of dust layers: dust layers composed of single particles (simple model) and dust layers consisting of individual aggregates (complex model). Additionally, we describe laboratory experiments, which were used to measure the heat conductivity of porous dust layers, in order to test the model. We found that the model predictions are in an excellent agreement with the experimental results, if we include radiative heat transport in the model. This implies that radiation plays an important role for the heat transport in porous materials. Furthermore, the influence of this new model on the Hertz factor are demonstrated and the implications of this new model on the modeling of cometary activity are discussed. Finally, the limitations of this new model are critically reviewed.Comment: Submitted to Icaru

Strain-induced kinetics of intergrain defects as the mechanism of slow dynamics in the nonlinear resonant response of humid sandstone bars

A closed-form description is proposed to explain nonlinear and slow dynamics effects exhibited by sandstone bars in longitudinal resonance experiments. Along with the fast subsystem of longitudinal nonlinear displacements we examine the strain-dependent slow subsystem of broken intergrain and interlamina cohesive bonds. We show that even the simplest but phenomenologically correct modelling of their mutual feedback elucidates the main experimental findings typical for forced longitudinal oscillations of sandstone bars, namely, (i) hysteretic behavior of a resonance curve on both its up- and down-slopes, (ii) linear softening of resonant frequency with increase of driving level, and (iii) gradual recovery (increase) of resonant frequency at low dynamical strains after the sample was conditioned by high strains. In order to reproduce the highly nonlinear elastic features of sandstone grained structure a realistic non-perturbative form of strain potential energy was adopted. In our theory slow dynamics associated with the experimentally observed memory of peak strain history is attributed to strain-induced kinetic changes in concentration of ruptured inter-grain and inter-lamina cohesive bonds causing a net hysteretic effect on the elastic Young's modulus. Finally, we explain how enhancement of hysteretic phenomena originates from an increase in equilibrium concentration of ruptured cohesive bonds that are due to water saturation.Comment: 5 pages, 3 figure

Gas transfer through clay barriers

Gas transport through clay-rocks can occur by different processes that can be basically subdivided into pressure-driven flow of a bulk gas phase and transport of dissolved gas either by molecular diffusion or advective water flow (Figure 1, Marschall et al., 2005). The relative importance of these transport mechanisms depends on the boundary conditions and the scale of the system. Pressure-driven volume flow (“Darcy flow”) of gas is the most efficient transport mechanism. It requires, however, pressure gradients that are sufficiently large to overcome capillary forces in the typically water-saturated rocks (purely gas-saturated argillaceous rocks are not considered in the present context). These pressure gradients may form as a consequence of the gravity field (buoyancy, compaction) or by gas generation processes (thermogenic, microbial, radiolytic). Dissolved gas may be transported by water flow along a hydraulic gradient. This process is not affected by capillary forces but constrained by the solubility of the gas. It has much lower transport efficiency than bulk gas phase flow. Molecular diffusion of dissolved gas, finally, is occurring essentially without constraints, ubiquitously and perpetually. Effective diffusion distances are, however, proportional to the square root of time, which limits the relevance of this transport process to the range of tens to hundreds of metres on a geological time scale (millions of years). 2 Process understanding and the quantification of the controlling parameters, like diffusion coefficients, capillary gas breakthrough pressures and effective gas permeability coefficients, is of great importance for up-scaling purposes in different research disciplines and applications. During the past decades, gas migration through fully water-saturated geological clay-rich barriers has been investigated extensively (Thomas et al., 1968, Pusch and Forsberg, 1983; Horseman et al., 1999; Galle, 2000; Hildenbrand et al., 2002; Marschall et al., 2005; Davy et al., 2009; Harrington et al., 2009, 2012a, 2014). All of these studies aimed at the analysis of experimental data determined for different materials (rocks of different lithotype, composition, compaction state) and pressure/temperature conditions. The clay-rocks investigated in these studies, ranged from unconsolidated to indurated clays and shales, all characterised by small pores (2-100 nm) and very low hydraulic conductivity (K < 10-12 m·s-1) or permeability coefficients (k < 10-19 m²). Studies concerning radioactive waste disposal include investigations of both the natural host rock formation and synthetic/engineered backfill material at a depth of a few hundred meters (IAEA, 2003, 2009). Within a geological disposal facility, hydrogen is generated by anaerobic corrosion of metals and through radiolysis of water (Rodwell et al., 1999; Yu and Weetjens, 2009). Additionally, methane and carbon dioxide are generated by microbial degradation of organic wastes (Rodwell et al., 1999; Ortiz et al., 2002; Johnson, 2006; Yu and Weetjens, 2009). The focus of carbon capture and storage (CCS) studies is on the analysis of the long-term sealing efficiency of lithologies above depleted reservoirs or saline aquifers, typically at larger depths (hundreds to thousands of meters). During the last decade, several studies were published on the sealing integrity of clay-rocks to carbon dioxide (Hildenbrand et al., 2004; Li et al., 2005; Hangx et al., 2009; Harrington et al., 2009; Skurtveit et al., 2012; Amann-Hildenbrand et al., 2013). In the context of petroleum system analysis, a significant volume of research has been undertaken regarding gas/oil expulsion mechanisms from sources rocks during burial history (Tissot & Pellet, 1971; Appold & Nunn, 2002), secondary migration (Luo et al., 2008) and the capillary sealing capacity of caprocks overlying natural gas accumulations (Berg, 1975; Schowalter, 1979; Krooss, 1992; Schlömer and Kross, 2004; Li et al., 2005; Berne et al., 2010). Recently, more attention has been paid to investigations of the transport efficiency of shales in the context of oil/gas shale production (Bustin et al., 2008; Eseme et al., 2012; Amann-Hildenbrand et al., 2012; Ghanizadeh et al., 2013, 2014). Analysis of the migration mechanisms within partly unlithified strata becomes important when explaining the 3 origin of overpressure zones, sub-seafloor gas domes and gas seepages (Hovland & Judd, 1988; Boudreau, 2012). The conduction of experiments and data evaluation/interpretation requires a profound process understanding and a high level of experience. The acquisition and preparation of adequate samples for laboratory experiments usually constitutes a major challenge and may have serious impact on the representativeness of the experimental results. Information on the success/failure rate of the sample preparation procedure should therefore be provided. Sample specimens “surviving” this procedure are subjected to various experimental protocols to derive information on their gas transport properties. The present overview first presents the theoretical background of gas diffusion and advective flow, each followed by a literature review (sections 2 and 3). Different experimental methods are described in sections 4.1 and 4.2. Details are provided on selected experiments performed at the Belgian Nuclear Research Centre (SCK-CEN, Belgium), Ecole Centrale de Lille (France), British Geological Survey (UK), and at RWTH-Aachen University (Germany) (section 4.3). Experimental data are discussed with respect to different petrophysical parameters outlined above: i) gas diffusion, ii) evolution of gas breakthrough, iii) dilation-controlled flow, and iv) effective gas permeability after breakthrough. These experiments were conducted under different pressure and temperature conditions, depending on sample type, burial depth and research focus (e.g. radioactive waste disposal, natural gas exploration, or carbon dioxide storage). The interpretation of the experimental results can be difficult and sometimes a clear discrimination between different mechanisms (and the controlling parameters) is not possible. This holds, for instance, for gas breakthrough experiments where the observed transport can be interpreted as intermittent, continuous, capillary- or dilation-controlled flow. Also, low gas flow rates through samples on the length-scale of centimetres can be equally explained by effective two-phase flow or diffusion of dissolved gas

Macroscopic Modeling of Polymer-Electrolyte Membranes

In this chapter, the various approaches for the macroscopic modeling of transport phenomena in polymer-electrolyte membranes are discussed. This includes general background and modeling methodologies, as well as exploration of the governing equations and some membrane-related topic of interest

Algebraic Attacks specialized to F2\mathbb{F}_2 (Diplomarbeit)

This thesis studies the ring of boolean functions. A simple algorithm that performs similarly to the euclidian algorithm is derived, and it\u27s performance for solving multivariate boolean equation systems is evaluated. Furthermore, the Raddum-Semaev equation system solving algorithm is put into geometric context, and the pseudo-euclidian algorithm is generalized to multivariate polynomial rings over arbitrary finite fields